If $\overrightarrow a=\hat i+\hat j-\hat k,\:\overrightarrow b=-\hat i+2\hat j+\hat k\:\:and\:\:\overrightarrow c=-\hat i+2\hat j-\hat k$, then a unit vector $\perp$ to $\overrightarrow a+\overrightarrow b$ and $\overrightarrow b+\overrightarrow c$ is ?

Question

$\begin{array}{1 1} (A) \hat i \\ (B) \hat j \\ (C) \hat k \\ (D) \large\frac{1}{\sqrt 3}(\hat i+\hat j+\hat k) \end{array} $