# How do you find a) u+v, b) u-v, c) 2u-3v given u=<-5,3>, v=<0,0>?

Feb 17, 2017

$< - 5 , 3 > , < - 5 , 3 > , < - 10 , 6 >$

#### Explanation:

$\left(a\right) \vec{u} + \vec{v} = < - 5 , 3 > + < 0 , 0 >$

Add the corresponding x and y components together.

$\Rightarrow \vec{u} + \vec{v} = < - 5 , 3 >$

$\left(b\right) \vec{u} - \vec{v} = < - 5 , 3 > - < 0 , 0 >$

Subtract the corresponding x and y components.

$\Rightarrow \vec{u} - \vec{v} = < - 5 , 3 >$

$\left(c\right) 2 \vec{u} - 3 \vec{v} = 2 < - 5 , 3 > - 3 < 0 , 0 >$

Multiply each component by the scalar.

$2 \vec{u} - 3 \vec{v} = < - 10 , 6 > - < 0 , 0 \ge < - 10 , 6 >$