If and are coplanar

MATHEMATICS · Subjective · A Level · Mathematics · Vectors · Vectors

Problem

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are coplanar, show that

\bigl[\mathbf{a} \times \mathbf{b},\, \mathbf{b} \times \mathbf{c},\, \mathbf{c} \times \mathbf{a}\bigr]

are coplanar.