If the position vectors of two points A and B | vedclass

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(D) Let the position vectors of points $A$ and $B$ be $\vec{p} = \vec{a} + 3\vec{b}$ and $\vec{q} = \vec{a} - 2\vec{b}$.Using the section formula for

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$\vec{a} + \frac{11}{7}\vec{b}$

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(D) Let the position vectors of points $A$ and $B$ be $\vec{p} = \vec{a} + 3\vec{b}$ and $\vec{q} = \vec{a} - 2\vec{b}$.Using the section formula for internal division in the ratio $m:n = 2:5$,the position vector $\vec{r}$ is given by:$\vec{r} = \frac{m\vec{q} + n\vec{p}}{m + n}$Substituting the values:$\vec{r} = \frac{2(\vec{a} - 2\vec{b}) + 5(\vec{a} + 3\vec{b})}{2 + 5}$$\vec{r} = \frac{2\vec{a} - 4\vec{b} + 5\vec{a} + 15\vec{b}}{7}$$\vec{r} = \frac{7\vec{a} + 11\vec{b}}{7}$$\vec{r} = \vec{a} + \frac{11}{7}\vec{b}$

If the position vectors of two points $A$ and $B$ are $\vec{a} + 3\vec{b}$ and $\vec{a} - 2\vec{b}$ respectively,find the position vector of the point that divides $AB$ in the ratio $2:5$.

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