• question_answer The position vector of a particle is $\vec{r}=(a\cos \omega t)\hat{i}+(a\sin \omega t)\hat{j}$. The velocity of the particle is                                                                    [CBSE PMT 1995] A)            Parallel to the position vector B)            Perpendicular to the position vector C)            Directed towards the origin D)            Directed away from the origin

$\vec{r}=(a\cos \omega \,t)\hat{i}+(a\sin \omega \,t)\hat{j}$                    $\vec{v}=\frac{d\vec{r}}{dt}=-a\omega \sin \omega \,t\,\hat{i}+a\omega \cos \omega \,t\,\hat{j}$            As $\vec{r}.\vec{v}=0$ therefore velocity of the particle is perpendicular to the position vector.