The inner product of a vector x with a bivector B

gives a vector x.B which is contained in the bivector plane of B, but perpendicular to the projection of x onto B, which is x_p = (x.B)/B.

You can change the vector x by interactively dragging the bright red point with the mouse.

Please enable Java for an interactive construction (with Cinderella).

The basic idea for this applet stems from the "DEMOinner" in Dorst, Mann and Bouma's geometric algebra MATLAB tutorial GABLE.

[ GA with Cinderella ]

Soli Deo Gloria. Created with Cinderella by E. Hitzer (Fukui).