Some geometrical properties of quaternions in Clifford algebra \(R_{3,0}\) (Q2564492)

Using the conjugation -- composition of main involution and main antiinvolution -- the author defines his ``integrated product'', a map \(\circ:\mathbb{H}\times\mathbb{H}\mapsto\mathbb{H}\), \(q_1\circ q_2=q_1\overline q_2\). Therefrom he derives the various geometric notations as parallelity, perpendicularity, angle, rotation etc. The situation appears as the algebra \(Cl_{3,0}\) with a mutated product, given by the ``integrated product''.