Surface Integral Homework: A.n dS in Plane 2x+y=6, z=4

[bon]

Homework Statement

So trying to find the Integral of A.n dS where A is (y,2x,-z) and S is the surface of the plane 2x+y = 6 in the first octant cut off by the plane z=4

Homework Equations

The Attempt at a Solution

So i always solve these by projection...but I am a bit confused this time..

normally the surface is in the form z=f(x,y) so i do z-f(x,y) and take grad to find the normal..

so is the normal vector here just (2,1)? ie. grad 2x-y-6 = 0?

In which case is the integral just the double integral of (y,2x,-4).(2,1,0) dA?

Im a bit confused..Any help would be great!

 

[bon]

Any ideas..?
I'm pretty confused about which plane you project onto to solve this...

Thanks!

 

[bon]

So do you project onto y-z plane?

and is the integral therefore the 1/2 times the double integral of A.(2,1,0) dydz?