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  4. If C is the mid point of AB and P is any point outside AB, then :

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Q. If $C$ is the mid point of $AB$ and $P$ is any point outside $AB$, then :

AIEEEAIEEE 2005Vector Algebra

Solution:

If $C$ is mid point of $AB$ and $P$ be the origin, then $\overrightarrow{PC}=\frac{\overrightarrow{PA}+\overrightarrow{PB} }{2}.$
Let $P$ be the origin outside of $AB$ and $C$ is mid point of $AB$, then
$\overrightarrow{PC}=\frac{\overrightarrow{PA}+\overrightarrow{PB} }{2}$
$\Rightarrow 2\overrightarrow{PC} =\overrightarrow{PA} +\overrightarrow{PB}$