# What Does Position Vector Mean?

Theory

### PositionVector

A vector that begins at the origin $O=\left(0,0\right)$ and extends to a point $P=\phantom{\rule{-0.17em}{0ex}}\left(x,y\right)$ is called a position vector. It’s written

 $\stackrel{\to }{OP}=\phantom{\rule{-0.17em}{0ex}}\left(x,y\right).$

Every point has a position vector. In this way, you can always rewrite a point as a vector. If the coordinates of the point is $P=\phantom{\rule{-0.17em}{0ex}}\left(x,y\right)$, the position vector is $\stackrel{\to }{OP}=\phantom{\rule{-0.17em}{0ex}}\left(x,y\right)$.

Example 1

Find the position vector that belongs to the point $P=\phantom{\rule{-0.17em}{0ex}}\left(-13,12\right)$

By using the formula for the position vector of a point, you get

 $\stackrel{\to }{OP}=\phantom{\rule{-0.17em}{0ex}}\left(-13,12\right).$