# How do you find a) u+v, b) u-v, c) 2u-3v given u=-2i+j, v=-i+2j?

Sep 19, 2017

See the answers below

#### Explanation:

This is the sum or difference of $2$ vectors and multiplication by a scalar

$\vec{u} = - 2 \hat{i} + \hat{j}$

$\vec{v} = - \hat{i} + 2 \hat{j}$

Therefore,

$\vec{u} + \vec{v} = \left(- 2 \hat{i} + \hat{j}\right) + \left(- \hat{i} + 2 \hat{j}\right) = - 3 \hat{i} + 3 \hat{j}$

$\vec{u} - \vec{v} = \left(- 2 \hat{i} + \hat{j}\right) - \left(- \hat{i} + 2 \hat{j}\right) = - \hat{i} - \hat{j}$

$2 \vec{u} - 3 \vec{v} = 2 \left(- 2 \hat{i} + \hat{j}\right) - 3 \left(- \hat{i} + 2 \hat{j}\right) = - \hat{i} - 4 \hat{j}$