Answer
$\theta =\dfrac{\pi}{2}$
Work Step by Step
Since, we have $r=\lt 3t+1, \sqrt 3t ,t^2 \gt$
Now, velocity $v(t)=r'(t)=\lt 3, \sqrt 3 ,2t \gt$
and $v(0)=\lt 3, \sqrt 3 ,0\gt = 3i +\sqrt 3 j$
As we know acceleration $a(t)=v'(t)=\lt 0,0,2 \gt$
and $a(0)=\lt 0,0,2 \gt= 2k$
Hence, we can see that $v(0)$ is in the xy plane and $a(0)$ is in the direction of k . Thus, we have $\theta =\dfrac{\pi}{2}$
