A particle moves so that its position vector is given by \( \vec{r}=\cos \omega t \hat{x}+\sin \...

A particle moves so that its position vector is given by \( \vec{r}=\cos \omega t \hat{x}+\sin \omega t \hat{y} \), where \( \omega \) is a constant. Which of the following is true
(a) Velocity and acceleration both are perpendicular to \( \vec{r} \)
(b) Velocity and acceleration both are parallel to \( \vec{r} \)
(c) Velocity is perpendicular to \( \vec{r} \) and acceleration is directed towards the origin
(d) Velocity is perpendicular to \( \vec{r} \) and acceleration is directed away from the origin