# How do you find a unit vector that is oppositely directed to v = (1, 3,- 4)?

Feb 20, 2017

$- \frac{1}{\sqrt{26}} < 1 , 3 , - 4 >$.

#### Explanation:

The opposite vector is $- \vec{v} = - < 1 , 3 , - 4 >$.

So, the unit vector in the opposite direction is

$\frac{1}{|} - \vec{v} | \left(- \vec{v}\right) = \frac{1}{\sqrt{{1}^{2} + {3}^{2} + {\left(- 4\right)}^{2}}} \left(- < 1 , 3 , - 4 >\right)$

$= - \frac{1}{\sqrt{26}} < 1 , 3 , - 4 >$.