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If $C$ is the mid-point of line segment $A B$ and $P$ is any point not on the line $A B$, then
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Verified Answer
The correct answer is:
$\mathbf{P A}-\mathbf{P C}=\mathbf{P C}-\mathbf{P B}$
Here, $\mathbf{P C}$ is median and median of $\triangle P A B$.
$\begin{aligned} & \therefore & \mathbf{P C} & =\frac{\mathbf{P A}+\mathbf{P B}}{2} \\ & \Rightarrow & 2 \mathbf{P C} & =\mathbf{P A}+\mathbf{P B} \\ & \Rightarrow & \mathbf{P A}-\mathbf{P C} & =\mathbf{P C}-\mathbf{P B}\end{aligned}$
$\begin{aligned} & \therefore & \mathbf{P C} & =\frac{\mathbf{P A}+\mathbf{P B}}{2} \\ & \Rightarrow & 2 \mathbf{P C} & =\mathbf{P A}+\mathbf{P B} \\ & \Rightarrow & \mathbf{P A}-\mathbf{P C} & =\mathbf{P C}-\mathbf{P B}\end{aligned}$
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