# What is the unit vector of this vector v = -2i + 5j?

Jul 15, 2016

$\textcolor{b l u e}{\vec{u} = - \frac{2}{\sqrt{29}} i + \frac{5}{\sqrt{29}} j}$ is a unit vector with the same direction as $\vec{v} = - 2 + 5 j$

#### Explanation:

The unit vector, $\vec{u}$ corresponding to a given vector $\vec{v}$ can be calculated by dividing the terms of $\vec{v}$ by the magnitude (length) of $\vec{v}$

$\textcolor{w h i t e}{\text{XXX}} \vec{u} = \frac{\vec{v}}{\left\mid \vec{v} \right\mid}$

$\left\mid \vec{v} \right\mid$ is calculated using the Pythagorean Theorem.
In this case with $\vec{v} = - 2 i + 5 j$
$\textcolor{w h i t e}{\text{XXX}} \left\mid \vec{v} \right\mid = \sqrt{{\left(- 2\right)}^{2} + {5}^{2}} = \sqrt{29}$