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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.

[ GA with Cinderella ]

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