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- StudyBlue
- North-carolina
- University of North Carolina - Charlotte
- Mathematics
- Mathematics 2241
- Gordon
- 10.2 - Vectors

Jason S.

If **u** and **v** are vectors positioned so the initial point of **v** is at the terminal point of **u**, then the sum: ______ is the vector from the initial point of u to the terminal point of **v**.**• u - v****• u + v**

If *c* is a scalar and **v** is a vector, then the scalar multiple *c***v** is the vector whose length is |*c*| times the length of **v** and whose direction is the same as v if **1) ____** and is opposite to **v** if **2) ____** .

1) (*c* > 0) or (*c* < 0) or (*c* = 0)

2) (*c* > 0) or (*c* < 0) or (*c* = 0)

1) *c* > 0

2) *c* < 0

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)

The __length__ of the 2-D vector **a** = 〈 a_{1}, a_{2}〉is

- |
**a**| = √(a_{1}^{2}+ a_{2}^{2}) - |
**a**| = √(a_{1}^{2}+ a_{2}^{2}+ a_{3}^{2})

|**a**| = √(a_{1}^{2} + a_{2}^{2})

The __length__ of the 3-D vector **a** =〈 a_{1}, a_{2}, a_{3}〉is:

- |
**a**| = √(a_{1}^{2}+ a_{2}^{2}+ a_{3}^{2}) - |
**a**| = √(a_{1}^{2}+ a_{2}^{2})

|**a**| = √(a_{1}^{2} + a_{2}^{2} + a_{3}^{2})

If **a** =〈a_{1},a_{2}〉then:

*c***a**=〈ca_{1}, ca_{2}〉*c***a**=〈ca_{1}+ ca_{2}〉

If **a** =〈a_{1},a_{2}〉then: **a** + **b** =

- 〈a
_{1}− b_{1}, a_{2}− b_{2}〉 - 〈a
_{1}+ b_{1}, a_{2}+ b_{2}〉

〈a_{1} + b_{1}, a_{2} + b_{2}〉

If **a** =〈a_{1},a_{2}〉then: **a** − **b** =

- 〈a
_{1}− b_{1}, a_{2}− b_{2}〉 - 〈a
_{1}+ b_{1}, a_{2}+ b_{2}〉

〈a_{1} − b_{1}, a_{2} − b_{2}〉

〈a_{1},a_{2},a_{3}〉+〈b_{1},b_{2},b_{3}〉=

- 〈a
_{1}+b_{1}, a_{2}+b_{2}, a_{3}+b_{3}〉 - 〈a
_{1}−b_{1}, a_{2}−b_{2}, a_{3}−b_{3}〉

〈a_{1}+b_{1}, a_{2}+b_{2}, a_{3}+b_{3}〉

〈a_{1},a_{2},a_{3}〉−〈b_{1},b_{2},b_{3}〉=

- 〈a
_{1}+b_{1}, a_{2}+b_{2}, a_{3}+b_{3}〉 - 〈a
_{1}−b_{1}, a_{2}−b_{2}, a_{3}−b_{3}〉

〈a_{1}−b_{1}, a_{2}−b_{2}, a_{3}−b_{3}〉

**b + a***c***a +***c***b**

**a + b****a**

**a + b***c***a**+*c***b**

**a***c*(*d***a**)*c*

c(*d***a**)

- (
**a**+**b**) +**c** **ab**+**ac**

(**a** + **b**) + **c**

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**a****0**

*c***a**+*c***b***c***a**+*d***a**

**a****b**+**a**

a

A **unit vector** is a vector whose length is 1. In general, if **a ≠ 0**, then the unit vector that has the same direction as **a** is:

**u**= 1 / |**a**|**u**= ( 1 / |**a**| ) (**a**) =**a**/ |**a**|

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