If and are any three vectors in space

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

Problem

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are any three vectors in space, then show that

(\mathbf{c} + \mathbf{b}) \times (\mathbf{c} + \mathbf{a}) \cdot (\mathbf{c} + \mathbf{b} + \mathbf{a}) = [\mathbf{a} \mathbf{b} \mathbf{c}]