What is the grad vector on the center(0.5,0.5,0) of the unit square [0,1] x [0,1] rotated by 45 deg around x axis?
The four coordinates and their function value after rotation are:
first point f(0, 0.14) = -0.35
second point f(1, 0.14) = -0.35
third point f(1, 0.85) = 0.35
fourth point f(0, 0.85) = 0.35
And the center remains as f(0.5, 0.5) =0
I assume gradient vector is always perpendicular to the surface but they way I calculated(below), is coming tangent to the surface. Could anyone explain what I have done wrong.
