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Homework Help: Functional relation between different functions of(x,y,z)

  1. Dec 8, 2008 #1
    1. The problem statement, all variables and given/known data

    I have two scalar functions u(x,y,z) and v(x,y,z) which are differentiable..Now it is required to prove that a necessary and sufficient condition for these two to be functionally related by equation F(u,v)=0 is [[tex]\nabla[/tex]u] [tex]\times[/tex] [[tex]\nabla[/tex]v]=0


    3. The attempt at a solution
    clearly the cross products of the gradients are zero that means they point in he same direction.But what about the tangent planes?and how to approach this problem?
     
  2. jcsd
  3. Dec 8, 2008 #2

    lurflurf

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    Homework Helper

    0=F
    0=grad(F)
    0=(Fu)grad(u)+(Fv)grad(v)
    so clearly we need
    0=grad(u)xgrad(v)
     
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