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Let \(\Vect{a} = \begin{pmatrix} a_1 \\ a_2 \\ a_3 \end{pmatrix}\), \(\Vect{b} = \begin{pmatrix} b_1 \\ b_2 \\ b_3 \end{pmatrix}\), and \(\Vect{c} = \begin{pmatrix} c_1 \\ c_2 \\ c_3 \end{pmatrix}\) be three vectors in space. Prove the distributive property of the vector product:$$ \Vect{a} \times (\Vect{b}+\Vect{c}) = (\Vect{a} \times \Vect{b}) + (\Vect{a} \times \Vect{c}) $$
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