A particle moves so that its position vector is given by $\overrightarrow{r}=\cos \omega t \hat{x}+\sin \omega t \hat{y}$. Where $\omega$ is a constant. Which of the following is true ?

Velocity and acceleration both are parallel to $\overrightarrow{r}$

Velocity and acceleration both are perpendicular to $\overrightarrow{r}$

Velocity is perpendicular to $\overrightarrow{r}$ and acceleration is directed towards the origin

Velocity is perpendicular to $\overrightarrow{r}$ and acceleration is directed away from the origin