If $\overrightarrow a = \hat i + \hat j + \hat k \: and \: \overrightarrow b = \hat j - \hat k,$ Find a vector $\overrightarrow c$ such that $\overrightarrow a$ x $\overrightarrow c = \overrightarrow b$ and $\overrightarrow a . \overrightarrow c = 3$.

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