Find the position vector of the point which d | vedclass

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

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$-5\vec{b}$

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(D) Let the position vectors of points $A$ and $B$ be $\vec{p} = 2\vec{a} - 3\vec{b}$ and $\vec{q} = 3\vec{a} - 2\vec{b}$ respectively. The formula for the position vector of a point dividing the join of two points with position vectors $\vec{p}$ and $\vec{q}$ externally in the ratio $m:n$ is given by $\vec{r} = \frac{m\vec{q} - n\vec{p}}{m - n}$. Here,$m = 2$ and $n = 3$. Substituting the values: $\vec{r} = \frac{2(3\vec{a} - 2\vec{b}) - 3(2\vec{a} - 3\vec{b})}{2 - 3}$ $\vec{r} = \frac{6\vec{a} - 4\vec{b} - 6\vec{a} + 9\vec{b}}{-1}$ $\vec{r} = \frac{5\vec{b}}{-1} = -5\vec{b}$ Thus,the position vector of the point is $-5\vec{b}$.

Find the position vector of the point which divides the join of the points with position vectors $2\vec{a} - 3\vec{b}$ and $3\vec{a} - 2\vec{b}$ externally in the ratio $2:3$.

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