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

Question

Dr. Abubacker · Accepted Answer

(c)
Let the position of $B$ is $\overrightarrow{\mathbf{r}}$.
$	herefore\ \overrightarrow{\mathbf{a}} = \frac{2\overrightarrow{\mathbf{r}} + 3(\overrightarrow{\mathbf{a}} + 2\overrightarrow{\mathbf{b}})}{2 + 3}$
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$\Rightarrow 5\overrightarrow{\mathbf{a}} = 2\overrightarrow{\mathbf{r}} + 3\overrightarrow{\mathbf{a}} + 6\overrightarrow{\mathbf{b}}$
$\Rightarrow \ 2\overrightarrow{\mathbf{r}} = 2\overrightarrow{\mathbf{a}} - 6\overrightarrow{\mathbf{b}}$
$	herefore\ \overrightarrow{\mathbf{r}} = \overrightarrow{\mathbf{a}} - 3\overrightarrow{\mathbf{b}}$

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

Explanation

Reviewed by Dr. Abubacker

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