Flux vector through a surface

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1. Sep 28, 2014

ex81

[Q] Find the integral that represents the flux of the vector F = <x^2z, x^z, x^2z> through the surface S given by z = Ax + By + C for 0 <= x <= a and 0 <= y <= a, where A, B, C, and a are positive constants.

From what I remember of the Flux.

F dot n, where n is a a vector perpendicular to the plane.
double integral F dot (ru cross rv) du dv

What I'm not remembering is how I get the n.

2. Sep 30, 2014

HallsofIvy

A vector perpendicular to a plane, given by Ax+ By+ Cz= D is <A, B, C>. Of course, your z= Ax+ By+ C is the same as Ax+ By- z= -C which has normal vector <A, B, -1>.

More generally, if you are given a surface by f(x,y,z)= constant, the vector perpendicular to that surface is $\nabla f$.