Answer
Plot $VI$
Work Step by Step
Given that $r(u,v)=uv^{2}i+u^{2}vj+(u^{2}-v^{2})k$
To find the grid curves corresponding to $v$ as constant, substitute $v=k$
Then $x=ukv^{2}$ and $z=(u^{2}-k^{2})$
Eliminating $u$ gives us $z=\frac{u^{2}}{k^{4}}-k^{2}$
This is a parabola parallel to $xz$ plane; only plot $VI$ contains parabolic grid curves.
