A sphere of radius 2 is centered at the origin.
It may be viewed as a parametrized surface: $\mathbf{r}(\theta,\phi) = (2 \cos\theta \sin\phi, 2 \sin\theta \sin\phi, 2 \cos\phi)$, a level surface of the function $f(x,y,z) = x^2 + y^2 + z^2$, or as the graph of the function $g(x,y) = \sqrt{4 - x^2 - y^2}$.
Consider the sphere at the point $(1.00000, 1.00000, 1.41421)$ (corresponding to $(\theta, \phi) = (\pi/4, \pi/4)$ ).

A) Find the normal vector $\mathbf{r}_\theta \times \mathbf{r}_\phi$ at the given point:
$($, , $)$
B) Find the gradient of $f$ at the indicated point:
$($, , $)$
They should be parallel ....