Let the vectors $\overrightarrow a, \overrightarrow b, \overrightarrow c$ be given as $a_1\hat i + a_2\hat j + a_3\hat k, \: b_1\hat i + b_2\hat j + b_3\hat k, \: c_1\hat i + c_2\hat j + c_3\hat k$. Then show that $\overrightarrow a × (\overrightarrow b + \overrightarrow c) = \overrightarrow a × \overrightarrow b + \overrightarrow a × \overrightarrow c$

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