# How do you find the unit vector in the direction of vecu = (2,1,-3)?

Mar 15, 2018

The unit vector in the direction of any given vector is the vector divided by its magnitude:

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

#### Explanation:

Given $\vec{u} = \left(2 , 1 , - 3\right)$

$| \vec{u} | = \sqrt{{2}^{2} + {1}^{2} + {\left(- 3\right)}^{2}}$

$| \vec{u} | = \sqrt{14}$

$\hat{u} = \frac{1}{\sqrt{14}} \left(2 , 1 , - 3\right)$

$\hat{u} = \frac{\sqrt{14}}{14} \left(2 , 1 , - 3\right)$

$\hat{u} = \left(2 \frac{\sqrt{14}}{14} , \frac{\sqrt{14}}{14} , - 3 \frac{\sqrt{14}}{14}\right)$