A particle moves such that its position
vector $\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$ where $\omega $ is a constant and t is time. Then which of the following statements is true for the velocity
$\overrightarrow v \left( t \right)$ and acceleration $\overrightarrow a \left( t \right)$ of the particle :
$\overrightarrow v $ and $\overrightarrow a $ both are perpendicular to $\overrightarrow r $
$\overrightarrow v $ and $\overrightarrow a $ both are parallel to $\overrightarrow r $
$\overrightarrow v $ is perpendicular to $\overrightarrow r $ and $\overrightarrow a $ is directed
towards the origin
$\overrightarrow v $ is perpendicular to $\overrightarrow r $ and $\overrightarrow a $ is directed
away from the origin
Solution
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