Tangent Plane and Normal Line using a gradient, Multivariable Calculus
We find the tangent plane equation at point (2,1,1) for a given three-variable equation and then determine the equation of the line normal to this plane at the same point. We approach this by treating the equation as a level surface of a function h, and calculate the gradient of h at (2,1,1) to get the orthogonal vector. Using this vector and the point, we can write down the equation for the tangent plane and normal line.
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