# How do you find the unit vector in the direction of the vector a = 2i + 3j?

Oct 26, 2016

$\vec{\hat{a}} = \frac{\sqrt{13}}{13} \left(2 \vec{i} + 3 \vec{j}\right)$

#### Explanation:

unit vector in direction of $\vec{a}$ is given by

$\vec{\hat{a}} = \frac{\vec{a}}{|} a |$

so for $\vec{a} = 2 \vec{i} + 3 \vec{j}$

$\vec{\hat{a}} = \frac{1}{\sqrt{{2}^{2} + {3}^{2}}} \left(2 \vec{i} + 3 \vec{j}\right)$

$\vec{\hat{a}} = \frac{1}{\sqrt{13}} \left(2 \vec{i} + 3 \vec{t} j\right)$

$\vec{\hat{a}} = \frac{\sqrt{13}}{13} \left(2 \vec{i} + 3 \vec{j}\right)$