Question

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. $7\mathbf{a} - 15\mathbf{b}$
• B. $7\mathbf{a} + 15\mathbf{b}$
• C. $2\pi/3$
• D. $15\mathbf{a} + 7\mathbf{b}$

Answer 1

Answer: (A)

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

Answer 2

$\overset{\rightarrow}{OP} = \frac{1(\overset{\rightarrow}{OB}) + 2(6\mathbf{b} - 2\mathbf{a})}{1 + 2}$

$\Rightarrow 3(\mathbf{a} - \mathbf{b}) = \overset{\rightarrow}{OB} + 12\mathbf{b} - 4\mathbf{a} \Rightarrow \overset{\rightarrow}{OB} = 7\mathbf{a} - 15\mathbf{b}$.