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Pearce_09
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the question is
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.
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.