Mathematics

Problem

Let the vectors

\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}