Answer
$\dfrac{1}{\sqrt 2}(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
Work Step by Step
Here, $v=\dfrac{1}{\sqrt6}i-\dfrac{1}{\sqrt6}j-\dfrac{1}{\sqrt6}k$
and $|v|=\sqrt{(\dfrac{1}{\sqrt6})^2+(\dfrac{-1}{\sqrt6})^2+(\dfrac{-1}{\sqrt6})^2}=\sqrt {\dfrac{25}{25}}=\dfrac{1}{\sqrt 2}$
The unit vector $\hat{\textbf{v}}$ can be calculated as: $\hat{\textbf{v}}=\dfrac{v}{|v|}$
Now, $\hat{\textbf{v}}=\dfrac{\dfrac{1}{\sqrt6}i-\dfrac{1}{\sqrt6}j-\dfrac{1}{\sqrt6}k}{\dfrac{1}{\sqrt 2}}=(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
Thus, $v=|v|\hat{\textbf{v}}=\dfrac{1}{\sqrt 2}(\dfrac{1}{\sqrt3}i-\dfrac{1}{\sqrt 3}j-\dfrac{1}{\sqrt 3}k)$
