In geometric algebra the (red) "meet" M of two planes (characterized by bivectors A and B)
can be calculated with the help of the join J.
The join of two non-parallel planes is simply the three dimensional space characterized by the
trivector volume unit J = I3 (pseudoscalar). The meet is then:
M = (B/J).A = (B/I3).A
You can change the orientation of B by interactively dragging the dark green vector B/I3 with the mouse.
The basic idea for this applet stems from the "DEMOmeetplanes" in Dorst, Mann and Bouma's geometric algebra MATLAB tutorial GABLE.
Soli Deo Gloria. Created with Cinderella by E. Hitzer (Fukui).