Answer
$\dfrac{1}{\sqrt 2}(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
Work Step by Step
Formula to find the unit vector $\hat{\textbf{v}}$ is: $\hat{\textbf{v}}=\dfrac{v}{|v|}$
Given: $v=\dfrac{1}{\sqrt6}i-\dfrac{1}{\sqrt6}j-\dfrac{1}{\sqrt6}k$; $|v|=\sqrt{(\dfrac{1}{\sqrt6})^2+(\dfrac{-1}{\sqrt6})^2+(\dfrac{-1}{\sqrt6})^2}=\dfrac{1}{\sqrt 2}$
Thus, $\hat{\textbf{v}}=\dfrac{(\dfrac{1}{\sqrt6}i-\dfrac{1}{\sqrt6}j-\dfrac{1}{\sqrt6}k)}{(\dfrac{1}{\sqrt 2})}=(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
and $v=|v|\hat{\textbf{v}}=\dfrac{1}{\sqrt 2}(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
