[Solution] For a function f[x, y, z], how does the gradient vector of f at a point P relate to the level surface of f through


Question: For a function \(\mathbf{f}[x, y, z]\), how does the gradient vector of \(f\) at a point \(P\) relate to the level surface of \(\mathbf{f}\) through \(\overline{\mathrm{P}^{\top}}\)

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