Three vectors

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

Problem

Three vectors

\mathbf{a}

\mathbf{b}

and

\mathbf{c}

are such that

|\mathbf{a}|\ne0

\mathbf{a}\times\mathbf{b}=3\mathbf{a}\times\mathbf{c}

|\mathbf{a}|=|\mathbf{b}|=1

, and

|\mathbf{c}|=\frac{1}{3}

. If the angle between

\mathbf{b}

and

\mathbf{c}

60^\circ

and

|\mathbf{b}-3\mathbf{c}|=\lambda|\mathbf{a}|

, find

\lambda