If $\overrightarrow a = \hat i + \hat j + \hat k, \overrightarrow b = 2\hat i - \hat j + 3\hat k$ and $\overrightarrow c = \hat i - 2\hat j + \hat k$, find a unit vector parallel to the vector $2\overrightarrow a - \overrightarrow b + 3\overrightarrow c$

Question

$\begin{array}{1 1} (A) \large\frac{1}{\sqrt{22}}(3\hat i +3\hat j+2\hat k) \\ (B) \large\frac{1}{\sqrt{22}}(3\hat i -3\hat j-2\hat k) \\ (C) \large\frac{1}{\sqrt{22}}(3\hat i +3\hat j-2\hat k) \\ (D) \large\frac{1}{\sqrt{22}}(3\hat i -3\hat j+2\hat k) \end{array} $