Mathematics

Problem

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are three non-zero vectors such that

\mathbf{a} \times \mathbf{b} = \mathbf{c}

and

\mathbf{b} \times \mathbf{c} = \mathbf{a}

, prove that

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are mutually at right angles and

|\mathbf{b}| = 1

and

|\mathbf{c}| = |\mathbf{a}|