Let $\overrightarrow a = 2\hat i + \hat k, \overrightarrow b = \hat i + \hat j + \hat k$ and $\overrightarrow c = 4\hat i - 3\hat j + 7\hat k$ be three vectors. Find a vector $\overrightarrow r$ which satisfies $\overrightarrow r$ x $\overrightarrow b = \overrightarrow c$ x $\overrightarrow b$ and $\overrightarrow r. \overrightarrow a =0.$

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