Consider the surface in R^3 with equation (x^2)(z^3) - cos(xy) = 2. Find the normal direction to this surface at the point (1,pi,1), and determine the equation of the tangent plane at the same point.

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- Jan 20th 2009, 06:37 AMmatty888Normal & tangent plane
Consider the surface in R^3 with equation (x^2)(z^3) - cos(xy) = 2. Find the normal direction to this surface at the point (1,pi,1), and determine the equation of the tangent plane at the same point.

- Jan 20th 2009, 07:57 AMqpmathelp
f = (x^2)(z^3) - cos(xy) - 2

grad(f) at (1,pi,1) will give you the normal vector

that will give you the d.r's a:b:c of the normal to the tangent plane

use a(x-1) +b(y-pi) +c(z-1) = 0 to get the equation of the tangent plane