The gradient of $f$ and a point $P$ on the level surface $f(x, y, z)=0$ are given. Find an equation for the tangent plane to the surface at the point $P.$ $$\text { grad } f=y z \vec{i}+x z \vec{j}+x y \vec{k}, P=(1,2,3)$$
Added by Lance A.
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We can do this by substituting the coordinates of P into the gradient function: grad f(P) = (1)(3)i + (1)(2)j + (1)(2)k = 3i + 2j + 2k Show more…
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