# How do you find a unit vector in the direction of v: v = - 5i + 2j?

Sep 22, 2016

$- \frac{5}{\sqrt{29}} i + \frac{2}{\sqrt{29}} j$.

#### Explanation:

A unit vector in the direction of $\vec{v}$, is denoted by $\hat{\vec{v}}$,

and, is defined by,

$\hat{\vec{v}} = \frac{\vec{v}}{|} | \vec{v} | | \text{, provided, } \vec{v} \ne \vec{0}$.

Here, $\vec{v} = - 5 i + 2 j = \left(- 5 , 2\right) \ne \vec{0}$

$\Rightarrow | | \vec{v} | | = \sqrt{{\left(- 5\right)}^{2} + {\left(2\right)}^{2}} = \sqrt{29}$.

$\therefore \hat{\vec{v}} = - \frac{5}{\sqrt{29}} i + \frac{2}{\sqrt{29}} j$.