If and are vectors such that

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

Problem

\mathbf{A}, \mathbf{B}

and

\mathbf{C}

are vectors such that

|\mathbf{B}| = |\mathbf{C}|

, prove that

\{(\mathbf{A} + \mathbf{B}) \times (\mathbf{A} + \mathbf{C})\} \times (\mathbf{B} \times \mathbf{C}) \cdot (\mathbf{B} + \mathbf{C}) = 0.