The position vector of the point which divide | vedclass

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(B) Let the position vectors of the two points be $\vec{p} = 2a - 3b$ and $\vec{q} = 3a - 2b$.The formula for the position vector of a point dividing

Vedclass · Accepted Answer

$\frac{12}{5}a - \frac{13}{5}b$

Vedclass · Answer

(B) Let the position vectors of the two points be $\vec{p} = 2a - 3b$ and $\vec{q} = 3a - 2b$.The formula for the position vector of a point dividing the join of two points with position vectors $\vec{p}$ and $\vec{q}$ internally in the ratio $m : n$ is given by $\vec{r} = \frac{m\vec{q} + n\vec{p}}{m + n}$.Here,$m = 2$,$n = 3$,$\vec{p} = 2a - 3b$,and $\vec{q} = 3a - 2b$.Substituting these values into the formula:$\vec{r} = \frac{2(3a - 2b) + 3(2a - 3b)}{2 + 3}$$\vec{r} = \frac{6a - 4b + 6a - 9b}{5}$$\vec{r} = \frac{12a - 13b}{5}$$\vec{r} = \frac{12}{5}a - \frac{13}{5}b$.Thus,the correct option is $B$.

The position vector of the point which divides the line segment joining the points with position vectors $2a - 3b$ and $3a - 2b$ internally in the ratio $2 : 3$ is:

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