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  4. If position vector of a point A is veca + 2 vecb and any point P( veca) divides AB in the ratio of 2: 3, then position vector of B is

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Q. 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

Vector Algebra

Solution:

Let position vector of $B$ be $\vec{r}$.
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$\therefore \vec{a}=\frac{2\vec{r}+3\left(\vec{a}+2\vec{b}\right)}{2+3}$
$\Rightarrow 5\vec{a}=2\vec{r}+3\vec{a}+6\vec{b}$
$\Rightarrow 2\vec{r}=2\vec{a}-6\vec{b}$
$\Rightarrow \vec{r}=\vec{a}-3\vec{b}$