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Prove that $\overrightarrow{a}.(\overrightarrow{b}+\overrightarrow{c})\times (\overrightarrow{a}+2\overrightarrow{b}+3\overrightarrow{c})=[\overrightarrow{a}\;\overrightarrow{b}\;\overrightarrow{c}].$

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