Question: EAS Let (mathcal{S}) be the surface with parametrization [ Phi(u, v)=((3+sin v) cos u,(3+sin v) sin u, v) ] for (0 leq u leq 2

EAS Let $\mathcal{S}$ be the surface with parametrization
\[
\Phi(u, v)=((3+\sin v) \cos u,(3+\sin v) \sin u, v)
\]
for $0 \leq u \leq 2 \pi, 0 \leq v \leq 2 \pi$. Using a computer algebra system:
(a) plot $\mathcal{S}$ from several different viewpoints. Is $\mathcal{S}$ best described as a "vase that holds water" or a "bottomless vase"?
(b) calculate the normal vector $\mathbf{N}(u, v)$.

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