Given the trajectory
$$r(t)=[A\cos(\omega t),B\sin(\omega t+\alpha)]$$
Prove that the angles between $\vec{r}, \vec{v}, \vec{a}$ are constant.
So the first idea is looking at the dot product and then (hopefully) $\cos(\theta), \theta$ being the angle of vectors, wouldn't have a time dependence. However doing all the extensive work it doesn't quite work. How could I do this?