Question

A and B are two points. The position vector of A is $6\,\overrightarrow{b}-2\,\overrightarrow{a}$ . A point P divides the line AB in the ratio 1 : 2. If $\overrightarrow{a}-\overrightarrow{b}$ is its position vector, then the position vector of B is given by

• A. $7\,\overrightarrow{a}-15\,\overrightarrow{b}$
• B. $7\,\overrightarrow{a}+15\,\overrightarrow{b}$
• C. $15\,\overrightarrow{a}-7\,\overrightarrow{b}$
• D. $15\,\overrightarrow{a}+7\,\overrightarrow{b}$

Answer 1

Answer: (A)

Let $B$ be the point $(\vec{r})$
$\therefore \frac{1\cdot\vec{r}+2\left(6\,\vec{b}-2\,\vec{a}\right)}{1+2}=\vec{a}-\vec{b}$
$\Rightarrow \vec{r}+12\,\vec{b}-4\,\vec{a}=3\,\vec{a}-4\,\vec{b}$

$6\,\vec{b}-2\,\vec{a}$
$\Rightarrow \vec{r}=7\,\vec{a}-15\,\vec{b}$
$\therefore B$ is $7\,\vec{a}-15\,\vec{b}$