Let , , and be unit vectors. Suppose that , and the angle between and is . Prove that…

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

Problem

Let

\mathbf{a}

\mathbf{b}

, and

\mathbf{c}

be unit vectors. Suppose that

\mathbf{a}\cdot\mathbf{b}=\mathbf{a}\cdot\mathbf{c}=0

, and the angle between

\mathbf{b}

and

\mathbf{c}

\frac{\pi}{6}

. Prove that

\mathbf{a}=\pm2(\mathbf{b}\times\mathbf{c})