Trivector as bivector c^a swept along vector b

A trivector (c^a)^b = a^b^c can according to Grassmann be visualized by displacing the bivector c^a parallel along the third linearly independent vector b. The resulting oriented volume of the paraleliped is the trivector.

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

Compare the two other ways to sweep out the same trivector: (a^b)^c and (b^c)^a.

[ GA with Cinderella ]

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