# How do you find the unit vector in the direction of v: v=4i-2j?

Sep 9, 2016

$\frac{4 i - 2 j}{2 \sqrt{5}}$

#### Explanation:

We have: $v = 4 i - 2 j$

Unit vectors are of the form $\hat{u} = \frac{u}{| u |}$:

$\implies \hat{v} = \frac{v}{| v |}$

$\implies \hat{v} = \frac{4 i - 2 j}{\sqrt{{\left(4\right)}^{2} + {\left(- 2\right)}^{2}}}$

$\implies \hat{v} = \frac{4 i - 2 j}{\sqrt{16 + 4}}$

$\implies \hat{v} = \frac{4 i - 2 j}{\sqrt{20}}$

$\implies \hat{v} = \frac{4 i - 2 j}{2 \sqrt{5}}$