# How do you normalize  (i -2j + 3k) ?

Dec 28, 2017

$\frac{1}{\sqrt{14}} \left(\hat{i} - 2 \hat{j} + 3 \hat{k}\right)$

#### Explanation:

to normalize a vector means to change it to a unit vector, that is ensure that its magnitude is $= 1$

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

we ahve

$\vec{a} = \hat{i} - 2 \hat{j} + 3 \hat{k}$

$| a | 14$

$= \sqrt{{1}^{2} + {2}^{2} + {3}^{2}} = \sqrt{14}$

$\hat{\vec{a}} = \frac{1}{\sqrt{14}} \left(\hat{i} - 2 \hat{j} + 3 \hat{k}\right)$