Mathematics

Problem

Let

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

be non-zero vectors such that

(\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = \frac{1}{3}|\mathbf{b}||\mathbf{c}|\mathbf{a}

. If

\theta

is an acute angle between the vectors

\mathbf{b}

and

\mathbf{c}

, then

\sin \theta

is equal to [AIEEE 2004] a.

\frac{1}{3}

\frac{\sqrt{2}}{3}

\frac{2}{3}

\frac{2\sqrt{2}}{3}