Field and Wave Electromagnetics 2nd Edition by David Cheng

Exercise 4

The equation in space of a plane containing the point ( x 1 , y 1 , z 1 ) can be written as
l ( x- x 1 ) + m ( y - y 1 )+ p ( z - z 1 ) = 0,
where l, m, and p are direction cosines of a unit normal to the plane:
a n = a x l + a y m + a z p.
Given a vector field F = a x + a y 2 + a z 3, evaluate the integral
over the square plane surface whose corners are at (0, 0, 2), (2, 0, 2), (2, 2, 0), and (0, 2, 0).