# Angles between normals at 2 points on a surface

1. Jan 19, 2012

### svishal03

I have been reading about the normal vector to a point on a surface.

http://mathworld.wolfram.com/NormalVector.html

Can anyone explain if I have normals to 2 points on a surface and I want to compute the inclinations between them, how would one proceed?

2. Jan 19, 2012

### chiro

Hey svishal03.

What do you mean by inclinations? Do you mean the angle between them?

3. Jan 20, 2012

### HallsofIvy

How you determine the angle between normals depends upon the way the surface is given. For example, if you are given f(x,y,z)= constant, the normals at $(x_0, y_0, z_0)$ and $(x_1, y_1, z_1)$ are given by $\nabla f(x_0, y_0, z_0)$ and $\nabla f(x_1, y_1, z_1)$. And, of course, the angle between those two vectors is given by their dot product: $cos^{-1}(\vec{u}\cdot\vec{v}/|\vec{u}||\vec{v}|)$.