# How do you normalize <0,2,0>?

May 21, 2016

Normalizing a vector involves dividing each of its elements by the length of the vector, so that we end up with a vector of unit length in the same direction as the original vector. In this case $< 0 , 1 , 0 >$.

#### Explanation:

First find the length of the original vector:

$l = \sqrt{{0}^{2} + {2}^{2} + {0}^{2}} = \sqrt{4} = 2$

Now divide each element by this length, and the normalised vector is $< \frac{0}{2} , \frac{2}{2} , \frac{0}{2} > = < 0 , 1 , 0 >$

This makes sense: our original vector was of length 2 in the $x$ (or ($j$) direction, and the normalised vector is in the same direction and of length $1$ unit.