# How would you find a unit vector in the direction v = 6i-2j?

Oct 19, 2016

$\vec{\hat{v}} = \left(\frac{\sqrt{10}}{10}\right) \left(3 \vec{i} - \vec{j}\right)$

#### Explanation:

A unit vector $\vec{\hat{x}}$ in the direction of $\vec{x}$is given by

$\vec{\hat{x}} = \frac{\vec{x}}{|} x |$

In this case we have:

$| v | = \sqrt{{6}^{2} + {2}^{2}} = \sqrt{40} = 2 \sqrt{10}$

So a unit vector in the direction of$\vec{v}$

$\vec{\hat{v}} = \left(\frac{1}{2 \sqrt{10}}\right) \left(6 \vec{i} - 2 \vec{j}\right) = \left(\frac{1}{\sqrt{10}}\right) \left(3 \vec{i} - \vec{j}\right)$

Rationalizing the denominator we end up with

$\vec{\hat{v}} = \left(\frac{\sqrt{10}}{10}\right) \left(3 \vec{i} - \vec{j}\right)$