The black vector is in fact (u ^ (q-p) ^ v)/(u ^ v).
You can drag the perpendicular support vectors p and q,
as well as the direction vectors of the line. Try to find directions
to drag p that maximize and minimize the change of the black vector.
Also make sure you change the directions of the lines, to verify that the construction still works!
(This is a 2-D construction mimicking a 3-D situation, so hidden line
removal does not work correctly.)
Created with Cinderella by Leo Dorst 20010716.