If $\overrightarrow u = 2\hat i + 2\hat j - \hat k$ and $\overrightarrow v = 6\hat i - 3\hat j + 2\hat k$, then a unit vector perpendiculat to both $\overrightarrow u$ and $\overrightarrow v$ is $$\begin{array} (A) \: \hat i - 10\hat j - 18\hat k \quad & (B) \: \frac{1}{\sqrt {17}} \bigg( \frac{1}{5}\hat i - 2\hat j -\frac{18}{5}\hat k \bigg) \\ (C)\: \frac{1}{\sqrt {473}} \bigg( 7\hat i - 10\hat j -18\hat k \bigg) \quad & (D)\: \frac{1}{\sqrt {425}} \bigg( \hat i - 10\hat j -18\hat k \bigg) \end{array}$$

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