Suppose that two surfaces are given by the equations
F(x, y, z) = c and G(x, y, z) = k.
Moreover, suppose that these surfaces intersect at the point (x0, y0, z0). Show that the surfaces are tangent at (x0, y0, z0) if and only if
∇F(x0, y0, z0)×∇G(x0, y0, z0) = 0.
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