# How do you find the unit vector in the direction of the given vector 6i-2j?

Oct 29, 2016

$\left(3 \frac{\sqrt{10}}{10}\right) \hat{i} - \left(\frac{\sqrt{10}}{10} \hat{j}\right)$ Please read the explanation.

#### Explanation:

Divide the given vector by the magnitude:

$| 6 \hat{i} - 2 \hat{j} | = \sqrt{{6}^{2} + {\left(- 2\right)}^{2}} = 2 \sqrt{10}$

(6hati - 2hatj)/(2sqrt(10)) = (3sqrt(10)/10)hati - (sqrt(10)/10)hatj)

Please observe that the magnitude of the resulting vector is 1:

$\sqrt{{\left(3 \frac{\sqrt{10}}{10}\right)}^{2} + {\left(- \left(\frac{\sqrt{10}}{10}\right) \hat{j}\right)}^{2}} = 1$