We can express sphere using parametric form. For example when sphere's radius is 1.
x = x($\phi, $$\theta$) = cos($\phi$)sin($\theta$)
y = y($\phi, $$\theta$) = cos($\phi$)cos($\theta$)
z = z($\phi, $$\theta$) = sin($\phi$)
In my book, the tangent plane's normal vector is n = $\frac {\partial p}{\partial \theta}$ × $\frac {\partial p}{\partial \phi}$ (p is any point on the sphere)
I could not prove this. How to prove it?
Why there is cross operation?