Mathematics

Problem

\mathbf{a}

and

\mathbf{b}

are non-zero and non-collinear vectors, then show that

\mathbf{a} \times \mathbf{b} = [\mathbf{a} \mathbf{b} \hat{i}] \hat{i} + [\mathbf{a} \mathbf{b} \hat{j}] \hat{j} + [\mathbf{a} \mathbf{b} \hat{k}] \hat{k}