Mathematics

Problem

Let

\vec{a}

\vec{b}

and

\vec{c}

be three non-zero vectors such that no two of them are collinear and

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

. If

\theta

is the angle between vectors

\vec{b}

and

\vec{c}

, then a value of

\sin \theta

is : (1)

\frac{2}{3}

(2)

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

(3)

\frac{1}{3}

(4)

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