# How do you find a unit vector in the same direction as a=(-10, 6, -7)?

Jun 13, 2017

Compute the magnitude and then divide each component by the magnitude.

#### Explanation:

Compute the magnitude:

$| \vec{a} | = \sqrt{{\left(- 10\right)}^{2} + {6}^{2} + {\left(- 7\right)}^{2}}$

$| \vec{a} | = \sqrt{100 + 36 + 49}$

$| \vec{a} | = \sqrt{185}$

To obtain the unit vector of $\vec{a} = \left(- 10 , 6 , - 7\right)$, we divide each component by $\sqrt{185}$ but we should rationalize $\frac{1}{\sqrt{185}}$ to $\frac{\sqrt{185}}{185}$:

$\hat{a} = \left(\frac{- 10 \sqrt{185}}{185} , \frac{6 \sqrt{185}}{185} , \frac{- 7 \sqrt{185}}{185}\right)$