# How do you find unit vector of a=(1, 2, -2) in direction of a?

Aug 6, 2016

$\frac{a}{| | a | |} = \left(\frac{1}{3} , \frac{2}{3} , - \frac{2}{3}\right)$

#### Explanation:

Divide by the length of the vector $a$.

$| | a | | = \sqrt{{1}^{2} + {2}^{2} + {\left(- 2\right)}^{2}} = \sqrt{1 + 4 + 4} = \sqrt{9} = 3$

So the unit vector is:

$\frac{a}{| | a | |} = \frac{1}{3} \left(1 , 2 , - 2\right) = \left(\frac{1}{3} , \frac{2}{3} , - \frac{2}{3}\right)$