# For the given vector: v = 3i - j + 2k, how do you write a unit vector in the direction of vector v?

$\frac{v}{| | v | |} = \frac{3}{\sqrt{15}} i - \frac{1}{\sqrt{15}} j + \frac{2}{\sqrt{15}} k$
$| | v | | = \sqrt{{3}^{2} + {\left(- 1\right)}^{2} + {2}^{2}} = \sqrt{9 + 1 + 4} = \sqrt{15}$
So the normalised vector in the direction of $v$ is:
$\frac{v}{| | v | |} = \frac{1}{\sqrt{15}} \left(3 i - j + 2 k\right) = \frac{3}{\sqrt{15}} i - \frac{1}{\sqrt{15}} j + \frac{2}{\sqrt{15}} k$