Find a unit vector perpendicular to each of the vectors $\overrightarrow a+\overrightarrow b \: and \: \overrightarrow a-\overrightarrow b$, where $\overrightarrow a=3\hat i+2\hat j +2 \hat k$ and $\overrightarrow b = \hat i + 2\hat j -2\hat k.$

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