# How do you find the unit vector in the direction of the vector a = 3i + 4j?

Aug 7, 2016

$\frac{1}{5} a$

#### Explanation:

The unit vector in the direction of

$a = r < \cos \theta , \sin \theta >$ is

$\left(\cos \theta , \sin \theta\right)$.

So, the unit vector is $\frac{1}{r} a$.

Here, it is $\frac{< 3 , 4 >}{|} < 3 , 4 > | = \frac{1}{\sqrt{{3}^{2} + {4}^{2}}} a = \frac{1}{5} a$