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 \(\mathbf{N}(u, v)\).