# How do you normalize  (3i - j - 2k) ?

Feb 26, 2017

Divide by its length to get:

$\frac{3 \sqrt{14}}{14} i - \frac{\sqrt{14}}{14} j - \frac{\sqrt{14}}{7} k$

#### Explanation:

Divide it by its length:

$\left\mid \left\mid 3 i - j - 2 k \right\mid \right\mid = \sqrt{{3}^{2} + {\left(- 1\right)}^{2} + {\left(- 2\right)}^{2}} = \sqrt{9 + 1 + 4} = \sqrt{14}$

So the unit length vector in the same direction as $3 i - j - 2 k$ is:

$\frac{1}{\sqrt{14}} \left(3 i - j - 2 k\right) = \frac{\sqrt{14}}{14} \left(3 i - j - 2 k\right)$

$\textcolor{w h i t e}{\frac{1}{\sqrt{14}} \left(3 i - j - 2 k\right)} = \frac{3 \sqrt{14}}{14} i - \frac{\sqrt{14}}{14} j - \frac{\sqrt{14}}{7} k$