Physics Book - User contributions [en]

Vectors

2015-12-04T21:31:12Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

A vector is an object with a magnitude and a direction.

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <x, y, z> or xi + yj - zk.
Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:29:00Z

Erobelo3:

Written by Elizabeth Robelo

A vector is an object with a magnitude and a direction.

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math><x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math><a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:28:16Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math><x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math><a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:25:58Z

Erobelo3: /* Examples */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:25:38Z

Erobelo3: /* References */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:24:58Z

Erobelo3: /* References */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://www.mathsisfun.com/algebra/vectors.html https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf ]

[https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:24:04Z

Erobelo3: /* References */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==
[https://www.mathsisfun.com/algebra/vectors.html]

[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:22:31Z

Erobelo3: /* See also */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:21:49Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:20:37Z

Erobelo3: /* A Computational Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

Here you have vpython code creating a vector from one object to another. [https://trinket.io/embed/glowscript/a8e75ad500 vectors]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:16:48Z

Erobelo3: /* References */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:16:30Z

Erobelo3: /* External links */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:15:58Z

Erobelo3: /* External links */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/][http://ocw.mit.edu/courses/mathematics/18-02sc-multivariable-calculus-fall-2010/1.-vectors-and-matrices/part-a-vectors-determinants-and-planes/session-1-vectors/MIT18_02SC_notes_0.pdf]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:09:41Z

Erobelo3: /* Connectedness */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
You will use vectors for everything in physics ranging from velocity to gravitational field.

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T21:08:26Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:40:29Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2.

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:39:49Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 21.21</math>

Finally divide the vector by its magnitude to get the unit vector:

<math>\tfrac{<12,-15,9>}{180}</math>

= <.565, -.707, .424>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:37:47Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\tfrac{<12,-15,9>}{180}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:36:16Z

Erobelo3: /* Middling */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> = C</math>

<math>\sqrt{(-6)^2 + 14^2 + 2^2} = 15.36</math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\frac{{<12,-15,9}{180}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:34:24Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\frac{{<12,-15,9}{180}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:31:56Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\frac{<12,-15,9}}{{180}}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:31:17Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\frac{\math{<12,-15,9}}{\|\math{180}\|}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:28:09Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>\sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>\frac{\mathbf{<12,-15,9}}{\|\mathbf{180}\|}</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T19:24:05Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?
First you have to find the magnitude of the vector given:
<math>sqrt{12^2 + (-15)^2 + 9^2} = 180</math>

Finally divide the vector by its magnitude to get the unit vector:
<math>(<12, -15, 9>)/180</math>

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:42:07Z

Erobelo3: /* Middling */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

A - B = <math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:40:34Z

Erobelo3: /* Middling */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

<math> <6-12, 21-7, 17-15> = <-6, 14, 2> </math>

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:32:59Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

The answer is 2 because

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:30:31Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

1. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>

2. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>

3. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>

4. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:29:46Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

a. <math>\overrightarrow{c} = \overrightarrow{b} + \overrightarrow{a}</math>
b. <math>\overrightarrow{a} = \overrightarrow{b} - \overrightarrow{c}</math>
c. <math>\overrightarrow{a} = \overrightarrow{b} + \overrightarrow{c}</math>
d. <math>\overrightarrow{b} = \overrightarrow{a} + \overrightarrow{c}</math>

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:28:19Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

c = b + a
a = b - c
a = b + c
b = a - c

<math>\overrightarrow{c}. = \overrightarrow{b}. + \overrightarrow{a}.</math>

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:19:34Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center]]

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:16:22Z

Erobelo3: /* Middling */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center|Adding vector A to B]]

===Middling===
What is the magnitude of the vector C = A - B if A = <6, 21, 17> and B = <12, 7, 15>?

===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

File:Simproblem.jpg

2015-12-04T15:08:27Z

Erobelo3:

Vectors

2015-12-04T15:08:10Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:simproblem.jpg|275px|thumb|center|Adding vector A to B]]

===Middling===
===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:07:08Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:problem1.jpg|275px|thumb|center|Adding vector A to B]]

===Middling===
===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:06:40Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

[[File:problem.jpg|275px|thumb|center|Adding vector A to B]]

===Middling===
===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T15:05:32Z

Erobelo3: /* Simple */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
Which of the following statements is correct?

===Middling===
===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T14:46:07Z

Erobelo3: /* Difficult */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
What is the unit vector in the direction of the vector <12, -15, 9>?

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T14:39:22Z

Erobelo3: /* The Main Idea */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. The magnitude of a vector is a scalar. A vector is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

A unit vector is a vector that points in the same direction as the original vector with magnitude 1. We usually designate the unit vector with a "hat" <math alt= r-hat>{\hat{\imath}}</math>. The unit vector is often called the normal vector.

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> {<a1, a2, a3> + <b1, b2, b3>} = {<a1 + b1, a2 + b2, a3 + b3>} </math>

Unit Vector: :<math alt= "u-hat equals the vector u divided by its length">\mathbf{\hat{u}} = \frac{\mathbf{u}}{\|\mathbf{u}\|}</math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
What is the magnitude of the vector <

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T14:38:05Z

Erobelo3: /* A Mathematical Model */

Vectors

2015-12-04T14:34:20Z

Erobelo3: /* The Main Idea */

Vectors

2015-12-04T14:33:48Z

Erobelo3: /* The Main Idea */

Vectors

2015-12-04T14:27:52Z

Erobelo3: /* Examples */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> \<a1, a2, a3> + \<b1, b2, b3> = \<a1 + b1, a2 + b2, a3 + b3> </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===
What is the magnitude of the vector <

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T13:44:27Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> \<a1, a2, a3> + \<b1, b2, b3> = \<a1 + b1, a2 + b2, a3 + b3> </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:37:46Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form <math> A = <x, y, z> or xi + yj - zk. </math>

Magnitude: <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

Addition of two vectors: <math> <a1, a2, a3> + <b1, b2, b3> = <a1 + b1, a2 + b2, a3 + b3> </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:35:07Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form A = <x, y, z> or xi + yj - zk.

Magnitude: : <math> |A| = \sqrt{x^2 + y^2 + z^2} </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:34:54Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form A = <x, y, z> or xi + yj - zk.

Magnitude: : <math> |A| = \sqr{x^2 + y^2 + z^2} </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:32:36Z

Erobelo3: /* A Mathematical Model */

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form A = <x, y, z> or xi + yj - zk.

Magnitude: : <math> |A| = sqrt(x^2 + y^2 + z^2) </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:31:01Z

Erobelo3:

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]



To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

Vectors are given by x, y, and z coordinates. They are written in the form A = <x, y, z> or xi + yj - zk.
Magnitude: : <math> |A| = sqrt{x^2 + y^2 + z^2} </math>

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Giusto Bellavitis abstracted the basic idea of a vector in 1835 when he established the concept of equipollence. He called any pair of line segments of the same length and orientation equipollent. He found a relationship and created the first set of vectors.

The name vector was given to us by William Rowan Hamilton as part of his system of quaternions. The vectors he used were three dimensional.

Several other mathematicians developed similar vector systems to those of Bellavitis and Hamilton in the 19th century. The system used by Herman Grassman is the one that is most similar to the one used today. He thought of ideas similar to the cross product and vector differentiation.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]

Vectors

2015-12-04T07:09:42Z

Erobelo3:

Written by Elizabeth Robelo

==The Main Idea==

A vector is an object with a magnitude and a direction. It is represented by an arrow. The length of the arrow is the vector’s magnitude and the direction the arrow points is its direction. The start of the arrow is called the tail. The end where the arrow head is located is called the head.

Vectors can be added and subtracted to each other. To add two vectors you put them head to tail. The connecting arrow starting from the tail of one to the head of the other is the new vector.

[[File:Addingvectors.jpg|275px|thumb|center|Adding vector A to B]]

To subtract two vectors reverse the direction of the one you want to subtract and continue to add them like shown before.



[[File:Subtractingvectors.jpg|350px|thumb|center|Subtracting vector B from A]]

===A Mathematical Model===

What are the mathematical equations that allow us to model this topic. For example <math>{\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net}</math> where '''p''' is the momentum of the system and '''F''' is the net force from the surroundings.

===A Computational Model===

How do we visualize or predict using this topic. Consider embedding some vpython code here [https://trinket.io/glowscript/31d0f9ad9e Teach hands-on with GlowScript]

==Examples==

Be sure to show all steps in your solution and include diagrams whenever possible

===Simple===
===Middling===
===Difficult===

==Connectedness==
#How is this topic connected to something that you are interested in?
#How is it connected to your major?
#Is there an interesting industrial application?

==History==

Put this idea in historical context. Give the reader the Who, What, When, Where, and Why.

== See also ==

Are there related topics or categories in this wiki resource for the curious reader to explore? How does this topic fit into that context?

===Further reading===

Books, Articles or other print media on this topic

===External links===
[http://www.scientificamerican.com/article/bring-science-home-reaction-time/]

==References==

This section contains the the references you used while writing this page

[[Category:Which Category did you place this in?]]