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