If $\overrightarrow a = 4\hat i + 5\hat j - \hat k, \overrightarrow b = \hat i - 4\hat j + 5\hat k, \overrightarrow c = 3\hat i + \hat j - \hat k,$ find a vector $\overrightarrow d$ , which is perpendicular to both $\overrightarrow a \: and \: \overrightarrow b \: and \: \overrightarrow d.\overrightarrow c = 21$.

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