# How do you normalize  <2,3,1>?

Mar 25, 2017

$\left\langle\frac{2}{\sqrt{14}} , \frac{3}{\sqrt{14}} , \frac{1}{\sqrt{14}}\right\rangle$

#### Explanation:

To normalize a vector we calculate the vector norm (its magnitude) and scale the vector by dividing by the norm to create a unit vector.

So let:

$\vec{u} = \left\langle2 , 3 , 1 ,\right\rangle$

Then we calculate the vector norm:

$| | \vec{u} | | = \sqrt{{2}^{2} + {3}^{2} + {1}^{2}}$
$\text{ } = \sqrt{4 + 9 + 1}$
$\text{ } = \sqrt{14}$

Now we scale the initial vector by dividing by the norm to get:

$| | \hat{u} | | = \frac{1}{\sqrt{14}} \setminus \left\langle2 , 3 , 1 ,\right\rangle$

$\text{ } = \left\langle\frac{2}{\sqrt{14}} , \frac{3}{\sqrt{14}} , \frac{1}{\sqrt{14}}\right\rangle$