# How do you find u=3/4v-w given v=<4,-3,5>, w=<2,6,-1> and z=<3,0,4>?

Jun 6, 2017

$u = \left\langle0 , - \frac{9}{4} , - \frac{1}{4}\right\rangle$

#### Explanation:

We have: $u = \frac{3}{4} v - w$

First, let's substitute the vector expressions in place of $v$ and $w$:

$R i g h t a r r o w u = \frac{3}{4} \left(4 i - 3 j + 5 k\right) - \left(3 i + 0 j + 4 k\right)$

Expanding the parentheses:

$R i g h t a r r o w u = 3 i - \frac{9}{4} j + \frac{15}{4} k - 3 i - 0 j - 4 k$

Collecting like vector components:

$R i g h t a r r o w u = 0 i - \frac{9}{4} j - \frac{1}{4} k$

$\therefore u = \left\langle0 , - \frac{9}{4} , - \frac{1}{4}\right\rangle$

Therefore, the vector $u$ is simplified to $\left\langle0 , - \frac{9}{4} , - \frac{1}{4}\right\rangle$.