Mathematics

Problem

Three vectors

\mathbf{a}

(

|\mathbf{a}| \neq 0

\mathbf{b}

and

\mathbf{c}

are such that

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

. Also,

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

and

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

. If the angle between

\mathbf{b}

and

\mathbf{c}

60^\circ

, then a.

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

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

\mathbf{a} = 6\mathbf{c} + 2\mathbf{b}

\mathbf{a} = 6\mathbf{c} - 2\mathbf{b}