Answer
Plot $I$
Work Step by Step
Given that $r(u,v)=ucosvi+usinvj+sinuk$ and $-\pi \leq u \leq \pi$
If we hold $u$ constant, then the cross sections will be circles at the plane of $sinu$.
If we hold $v$ constant, then the grid curves will be $x=ucosv$ and $y=usinv$, which implies that:
$y=tanvx$
Therefore, the plot must be plot $I$, since no other plot has this shape.