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

Question

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

Accepted Answer

$\overrightarrow{PA}+\overrightarrow{AC}+\overrightarrow{CP}=\vec0$ \ldots (i), $\overrightarrow{PB}+\overrightarrow{BC}+\overrightarrow{CP}=\vec0$ \ldots (ii). Adding, and using $\overrightarrow{AC}=-\overrightarrow{BC}$ ($C$ is midpoint):

$$\overrightarrow{PA}+\overrightarrow{PB}+2\overrightarrow{CP}=\vec0 \implies \overrightarrow{PA}+\overrightarrow{PB}=2\overrightarrow{PC}$$

Solutions · 1