Question

If position vector of a point $A$ is $\vec{a}+2\vec{b}$ and any point $P(\vec{a})$ divides $\overrightarrow{AB}$ in the ratio of $2:3$, then position vector of $B$ is

• A. $2\vec{a}-\vec{b}$
• B. $\vec{b}-2\vec{a}$
• C. $\vec{a}-3\vec{b}$
• D. $\vec{b}$

Answer 1

Answer: (C)

Let position vector of $B$ be $\vec{r}$.

$\therefore \vec{a}=\frac{2\vec{r}+3\left(\vec{a}+2\vec{b}\right)}{2+3}$
$\Rightarrow 5\vec{a}=2\vec{r}+3\vec{a}+6\vec{b}$
$\Rightarrow 2\vec{r}=2\vec{a}-6\vec{b}$
$\Rightarrow \vec{r}=\vec{a}-3\vec{b}$