Let S1 be the level surface given by the equation f(x,y,z) =k1and letS2be the level surface...

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Let S1 be the level surface given by the equation f(x,y,z)=k1and letS2be the level surface given by the equation g(x,y,z)=k2. Suppose that C is the curve of intersection of thesurfacesS1andS2andassume that P is a point on C. show that anytangent vector to C at P must be parallel to?f(P)×?g(P)

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