# How do you find the unit vector of v=4i+2j?

Nov 28, 2016

The answer is $= \frac{2}{\sqrt{5}} i + \frac{1}{\sqrt{5}} j$

#### Explanation:

The unit vector of $\vec{v}$ is

hatv=vecv/(∥vecv∥)

vecv=4i+2j=〈4,2〉

∥vecv∥=sqrt(16+2)=sqrt20=2sqrt5

Therefore,

hatv=1/(2sqrt5)〈4,2〉=〈2/sqrt5,1/sqrt5〉

Nov 28, 2016

$\left(\frac{4}{\sqrt{20}} , \frac{2}{\sqrt{20}}\right)$

#### Explanation:

$\vec{v}$ is (4,2) Its magnitude $| | \vec{v} | | = \sqrt{{4}^{2} + {2}^{2}} = \sqrt{20}$

Hence unit vector would be $\left(\frac{4}{\sqrt{20}} , \frac{2}{\sqrt{20}}\right)$