# How do you normalize <0, 4, 4>?

The normalized vector is

$\frac{v}{|} v |$

where $| v | = \sqrt{{u}_{x}^{2} + {u}_{y}^{2} + {u}_{z}^{2}}$

hence $| v | = \sqrt{{0}^{2} + {4}^{2} + {4}^{2}}$ or $| v | = 4 \cdot \sqrt{2}$

Hence

$\frac{v}{|} v | = \left(\frac{0}{4 \cdot \sqrt{2}} , \frac{4}{4 \cdot \sqrt{2}} , \frac{4}{4 \cdot \sqrt{2}}\right)$

$\frac{v}{|} v | = \left(0 , \frac{1}{\sqrt{2}} , \frac{1}{\sqrt{2}}\right)$