I have no reason to think that ##\nabla f(x,y,z)=\lambda(x,y,z)## - although I could solve this if I could assume that. The conditions, as far as I can tell, just say that for some scalar field ##h## we have that ##\nabla f(x,y,z) = [h(x,y,z)](x,y,z)##. In particular, I tried this approach: Let...