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Let f and g be functions R^3 -> R. suppose f is differentiable and

df(x,y,z) = ( df/dx , df/dy , df/dz ) = g(x,y,z)(x,y,z)

show that f is constant on any sphere of radius r centered at the origin defined by x^2 + y^2 + z^2 = r^2.

this means to show that F is the level curves S: x^2 + y^2 + z^2 = r^2. You do this by showing that the gradient of f is normal to f; therefore the inner (dot) product of the gradient of f and the tangential vector is equal to 0

But i have no idea how to do it. Please help

thanks

A.P.

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# Homework Help: Let f and g be functions R^3 -> R

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