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

Aug 14, 2017

$\hat{v} = - \sqrt{\frac{2}{3}} \hat{i} - \frac{1}{\sqrt{6}} \hat{j} - \frac{1}{\sqrt{6}} \hat{k}$

#### Explanation:

Normalization of a vector is the process of finding a unit vector in the same direction of the vector in question.

The equation for the normalization of a vector (which I'll call $\vec{v}$) is given by

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

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

The magnitude of $\vec{v}$ is

||vecv|| = sqrt((-2)^2 + (-1)^2 + (-1)^2) = color(red)(ul(sqrt6

Thus, the unit vector ($\hat{v}$) will be

$\hat{v} = \frac{- 2}{\textcolor{red}{\sqrt{6}}} \hat{i} - \frac{1}{\textcolor{red}{\sqrt{6}}} \hat{j} - \frac{1}{\textcolor{red}{\sqrt{6}}} \hat{k}$

color(blue)(ulbar(|stackrel(" ")(" "hatv = -sqrt(2/3)hati - 1/(sqrt6)hatj - 1/(sqrt6)hatk" ")|)