Let $\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k$ . Find a vector $\overrightarrow d$ which is perpendicular to both $\overrightarrow a$ and $\overrightarrow b$ , and $\overrightarrow c ⋅ \overrightarrow d =15$

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