For given vectors, $ \overrightarrow a=2\hat i − \hat j + 2\hat k$ and $ \overrightarrow b=−\hat i + \hat j − \hat k$, find the unit vector in the direction of the vector $ \overrightarrow a +\overrightarrow b.$

Question

$\begin{array}{1 1}(A) \large \frac{-1}{\sqrt 2}\hat i-\large\frac{1}{\sqrt 2}\hat k \\(B) \large \frac{1}{\sqrt 2}\hat i-\large\frac{1}{\sqrt 2}\hat k \\ (C) \large \frac{-1}{\sqrt 2}\hat i+\large\frac{1}{\sqrt 2}\hat k \\(D) \large \frac{1}{\sqrt 2}\hat i+\large\frac{1}{\sqrt 2}\hat k \end{array} $