1. Nov 21, 2008

Greetings,
I'm having trouble deciding what to do, and in what order for this question:

Suppose F = F( x, y, z ) is a gradient field with F = $$\nabla$$f, S is a level surface of f, and C is a curve on S. What is the value of the line integral (over C) of F.dr ?

I think I'm a little confused since there are no values to work with... I'm assuming the level surface of f is referring to $$\nabla$$f, meaning that S is a surface of the gradients?

Any help would be appreciated, I'm mighty confused. :)

2. Nov 21, 2008

### Dick

They mean that C is contained in a level surface of f. I.e. f(c) is constant for c in C. Dotting grad(f) with a direction vector tells you how fast f is changing in that direction, doesn't it?

3. Nov 21, 2008