What is Position vector?

In a frame equipped with an origin $O$ and axes $Ox$, $Oy$, the position vector of a moving point $M$ at time $t$ is $\vect{OM}(t)$, of coordinates $\bigl(x(t),\, y(t)\bigr)$: two functions of time, one per axis. The curve traced by $M$ as $t$ runs is its trajectory.