The first thing I would do is draw a two dimensional version- two lines meeting at the origin with angle . That means that each line makes angle with the y-axis and so angle with the x-axis. One line has slope and the other has slope . If you are in the xz-plane, that would give equations for one of the lines. Now rotate the whole thing about the z- axis, letting "x" become "r" in cylindrical coordinates: .

Your two vectors, A= i+ k and B= -i+ k make angle with both axes and angle between them of 90 degrees (which is correct for the question "What is the vertex angle for z = sqrt(x^2+x^2)?").

, not -1.