What is the vector perpendicular to the surface given by z = Ax + By + C?

[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 (r_u cross r_v) du dv

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

 

[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.