A position vector is a vector used to represent the point of a point (in the Cartesian plane when working in 2D space) relative to the origin.
$\vec{OP} = 3i+2j$, from the origin.
Don't forget that the vector $\vec{OP}$ itself has no fixed position. It is not necessarily be attached to the origin, but instead describes the point P from the origin
Using position vectors enables you to use vector arithmetic or vector algebra as a general approach to solving problems in coordinate geometry.
This is good when we are dealing with points in the cartesian plane, and we have to solve using vectors.
$\vec{AB}= \vec{OB}-\vec{OA}$
Proof: $\vec{AB}=\vec{AO}+\vec{OB}$ We know $\vec{XY}=-\vec{YX}$ Hence, $\vec{AO} = - \vec{OA}$ Hence, $\vec{AB}=-\vec{OA}+\vec{OB}$ $\vec{AB}=\vec{OB}-\vec{OA}$ as required
