Mathematics

Problem

A and B are two points. The position vector of A is

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

. A point P divides the line AB in the ratio 1 : 2. If

\mathbf{a} - \mathbf{b}

is the position vector of P, then the position vector of B is given by a.

7\mathbf{a} - 15\mathbf{b}

7\mathbf{a} + 15\mathbf{b}

15\mathbf{a} - 7\mathbf{b}

15\mathbf{a} + 7\mathbf{b}