Let Ax,By be two perpendicular semi-straight lines, being not complanar, (non-coplanar rays) such that AB is the their common perpendicular, and let M and N be the two variable points on Ax and Bx, respectively, such that AM \plus{} BN \equal{} MN.
(a) Prove that there exist infinitely many lines being co-planar with each of the straight lines MN.
(b) Prove that there exist infinitely many rotations around a fixed axis δ mapping the line Ax onto a line coplanar with each of the lines MN. geometrygeometric transformationrotationgeometry unsolved