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

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(C) Let the position vectors of points $A$ and $B$ be $\vec{OA} = \vec{a} - 3\vec{b}$ and $\vec{OB} = 6\vec{b} - 2\vec{a}$.According to the section fo

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$\vec{0}$

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(C) Let the position vectors of points $A$ and $B$ be $\vec{OA} = \vec{a} - 3\vec{b}$ and $\vec{OB} = 6\vec{b} - 2\vec{a}$.According to the section formula,the position vector of a point $P$ dividing the line segment $AB$ in the ratio $m : n$ is given by $\vec{OP} = \frac{m\vec{OB} + n\vec{OA}}{m + n}$.Here,$m = 1$ and $n = 2$.Substituting the values:$\vec{OP} = \frac{1(6\vec{b} - 2\vec{a}) + 2(\vec{a} - 3\vec{b})}{1 + 2}$$\vec{OP} = \frac{6\vec{b} - 2\vec{a} + 2\vec{a} - 6\vec{b}}{3}$$\vec{OP} = \frac{\vec{0}}{3} = \vec{0}$.Thus,the position vector of the point is $\vec{0}$.

If the position vectors of two points $A$ and $B$ are $\vec{a} - 3\vec{b}$ and $6\vec{b} - 2\vec{a}$ respectively,then the position vector of the point dividing $AB$ in the ratio $1 : 2$ is:

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