# How do you normalize  (-5i + 12j+ 2 k)?

Jan 24, 2016

Normalizing a vector means making a unit vector in the same direction by dividing each component of the vector by the length of the original vector. In this case the normalized vector is  (−5/sqrt(173)i+12/sqrt(173)j+2/sqrt(173)k)

#### Explanation:

First find the length of the vector. If a vector is $\left(a i + b k + c j\right)$ its length is given by:

l=sqrt(a^2+b^2+c^2

The length of the given vector,  (−5i+12j+2k), is:

$l = \sqrt{{\left(- 5\right)}^{2} + {12}^{2} + {2}^{2}} = \sqrt{173} = 13.2$

We can express the normalized vector in two equivalent ways:

 (−5/sqrt(173)i+12/sqrt(173)j+2/sqrt(173)k)

OR

 (−5/13.2i+12/13.2j+2/13.2k)