What Is the Value of the Line Integral Over a Curve on a Level Surface?

[Damascus Road]

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. :)

 

[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?

 

[Damascus Road]

Ok, someone just explained to me that it is 0, since it's a conservative force.

I was having trouble interpreting S being a level surface of a gradient field, I'm still trying to figure that part out.

 

[Dick]

S is NOT a level surface of the gradient, it's a level surface of f. That's what the question SAID. And there's an even easier reason to say that it's zero (and it's zero even if C isn't closed). What the dot of the gradient vector and the tangent vector to C?