Answer
$t=0; t=\dfrac{\pi}{2}; t =\pi$
Work Step by Step
$v(t)=\dfrac{dr}{dt}$
and $v(t)=3 \cos t \ k -5 \sin t j$
Now, $a(t)=\dfrac{dv(t)}{dt}$
or, $a(t)=-3 \sin t \ k -5j \cos t $
Now, $v(t) \times a(t)=(3 \cos t \ k -5 \sin t j) \times (-3 \sin t \ k -5j \cos t) =16 \sin t \ \cos t $
Consider $v (t)\times a (t)=0$
This implies that: $16 \sin t \ \cos t =0$
Either $\sin t =0$ or, $\cos t=0$
Therefore, $t=0; t=\dfrac{\pi}{2}; t =\pi$
