If and are two non-collinear vector such that

MATHEMATICS · Subjective · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

\mathbf{b}

and

\mathbf{c}

are two non-collinear vector such that

\mathbf{a} \parallel (\mathbf{b} \times \mathbf{c})

, then prove that

(\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{a} \times \mathbf{c})

is equal to

|\mathbf{a}|^2 (\mathbf{b} \cdot \mathbf{c})