# How do you normalize <0, 1, 3>?

Aug 7, 2017

$\hat{v} = < 0 , \frac{1}{\sqrt{10}} , \frac{3}{\sqrt{10}} >$

#### Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of that vector (with magnitude (or "norm") $1$). It is found by the equation

$\underline{\overline{| \stackrel{\text{ ")(" "hatv = (vecv)/(||vecv||)" }}{|}}}$

where

$\hat{v}$ denotes the unit vector

$| | \vec{v} | |$ is the magnitude of vector $\vec{v}$

The magnitude of $\vec{v}$ is given by

||vecv|| = sqrt(0^2 + 1^2 + 3^2) = color(red)(ul(sqrt10

Thus, we have

hatv = (< 0,1,3 >)/(color(red)(sqrt10)) = color(blue)(ulbar(|stackrel(" ")(" "< 0, 1/(sqrt10), 3/(sqrt10) >" ")|)