Answer
$\dfrac{3}{7}i-\dfrac{6}{7}j -\dfrac{2}{7} k$
Work Step by Step
The magnitude of any vector (let us say $v$) can be determined using the formula
$||v||=\sqrt{p^2+q^2+r^2} $
and the unit vector $u$ in the same direction as $v$ can be found as: $u=\dfrac{v}{||v||}$
Therefore, the unit vector $u$ in the same direction as $v$ is:
$u=\dfrac{3i-6j-2k}{\sqrt {(3)^2+(-6)^2+(-2)^2}} =\dfrac{3i-6j-2k}{\sqrt {9+36+4}} =
\dfrac{3i-6j-2k}{7}=\dfrac{3}{7}i-\dfrac{6}{7}j -\dfrac{2}{7} k$