If the position vector of a point A is a + 2b | vedclass

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(C) Let the position vector of point $A$ be $\vec{OA} = a + 2b$.Let the position vector of point $P$ be $\vec{OP} = a$.Let the position vector of poin

Vedclass · Accepted Answer

$a - 3b$

Vedclass · Answer

(C) Let the position vector of point $A$ be $\vec{OA} = a + 2b$.Let the position vector of point $P$ be $\vec{OP} = a$.Let the position vector of point $B$ be $\vec{OB} = x$.Since $P$ divides $AB$ in the ratio $2:3$,by the section formula:$\vec{OP} = \frac{2(\vec{OB}) + 3(\vec{OA})}{2 + 3}$$a = \frac{2x + 3(a + 2b)}{5}$$5a = 2x + 3a + 6b$$2x = 5a - 3a - 6b$$2x = 2a - 6b$$x = a - 3b$Therefore,the position vector of $B$ is $a - 3b$.

If the position vector of a point $A$ is $a + 2b$ and a point $P$ divides $AB$ in the ratio $2:3$,where the position vector of $P$ is $a$,then the position vector of $B$ is:

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