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:
$u=\dfrac{-6i+12j+4k}{\sqrt {(-6)^2+(12)^2+(4)^2}} =\dfrac{-6i+12j+4k}{\sqrt {36+144+16}} \\=-\dfrac{3}{7}i +\dfrac{6}{7}j +\dfrac{2}{7} k$
