Let S be a simple parametrically defined surface with boundary C as in Stokes' Theorem. Let f and g be two continuously differentiable scalar fields defined on S. Let n be a choice of unit normal on S. If grad(f) is perpendicular to grad(g) x n everywhere on S, show that integral of fgrad(g)*dr=0.
Note: x is cross product and * is dot product
integral of F*dr=integral of curlF*ndS
The Attempt at a Solution
I'm pretty confused on this one.
First off, what does the perpendicular part mean? What does it tell me? Doesn't it just tell me that the cross product exists everywhere? How does this information help me solve the problem and show that the integration equals zero?