Let the vector \(\vec{a},\; \vec{b},\; \vec{c}\) 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 \(\vec{a} \times (\vec{b} + \vec{c}) = \vec{a} \times \vec{b} + \vec{a} \times\vec{c}\)