The light blue bivector x.I3 is the dual of the blue vector x. x is perpendicular to x.I3. The yellow vector (x.I3).I3 is the dual of the bivector x.I3. The vector (x.I3).I3 is antiparalell to x, because I3.I3 = -1.
You can change the position of x by interactively dragging its bright red endpoint with the mouse.
The basic idea for this applet stems from the "DEMOdual" in Dorst, Mann and Bouma's geometric algebra MATLAB tutorial GABLE.
Soli Deo Gloria. Created with Cinderella by E. Hitzer (Fukui).