0
$\begingroup$

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?

  • 0
    The cross product gives as output a vector perpendicular to the terms involved. – 2017-01-13
  • 0
    I knew the fact but instead, I wonder why it used partial differentials – 2017-01-14
  • 0
    A partial differential is a derivative along a direction. You are cross-multiplying two vectors tangential to the surface. – 2017-01-14

0 Answers 0