# How do you find the magnitude of <2,-6> and write it as a sum of the unit vectors?

Aug 13, 2017

$| | \left\langle2 , - 6\right\rangle | | = 2 \sqrt{10}$

$\left\langle2 , - 6\right\rangle = 2 \boldsymbol{\underline{\hat{i}}} - 6 \boldsymbol{\underline{\hat{j}}}$

#### Explanation:

The magnitude is given by the vector norm:

$| | \left\langle2 , - 6\right\rangle | | = \sqrt{{\left(2\right)}^{2} + {\left(- 6\right)}^{2}}$
$\text{ } = \sqrt{4 + 36}$
$\text{ } = \sqrt{40}$
$\text{ } = 2 \sqrt{10}$

And in unit vector form, we have:

$\left\langle2 , - 6\right\rangle = 2 \boldsymbol{\underline{\hat{i}}} - 6 \boldsymbol{\underline{\hat{j}}}$