(adsbygoogle = window.adsbygoogle || []).push({}); 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?

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

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