Right angle rotation with unit bivector I

The multiplication with the (orange or violet) unit bivector I = e1e2 = e1^e2 causes a 90 degree right angle rotation of the light blue unit vector e1 into the orthogonal light green unit vector e2 = e1.I and in the very same way a rotation of the blue vector x into the orthogonal green vector xI=x.I

The reason becomes obvious if we regard it as a special case of general inner product of vectors and bivectors: The vector x is in the plane of the bivector I, which itself is of unit magnitude.

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

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

[ GA with Cinderella ]

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