# How do you normalize (i+k)?

Jan 3, 2016

Divide by the scalar $\left\mid i + k \right\mid = \sqrt{2}$ to get:

$\frac{\sqrt{2}}{2} i + \frac{\sqrt{2}}{2} k$

#### Explanation:

$\left\mid i + k \right\mid = \sqrt{{1}^{2} + {1}^{2}} = \sqrt{2}$

So multiplying by $\frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ we find:

$\left\mid \frac{\sqrt{2}}{2} i + \frac{\sqrt{2}}{2} k \right\mid = \sqrt{{\left(\frac{\sqrt{2}}{2}\right)}^{2} + {\left(\frac{\sqrt{2}}{2}\right)}^{2}}$

$= \sqrt{\frac{1}{2} + \frac{1}{2}} = \sqrt{1} = 1$