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1) Let P,Q be planes through the origin in R3. Let Rp, Rq be the corresponding reflections. Is Rp*Rq (where * denotes "composition") in SO(3) or O(3)/SO(3)? What is the axis of rotation of Rp*Rq?
2) For a fixed A in SO(3) show that there are infinitely many pairs of planes P,Q such that A=Rp*Rq.
3) For arbitrary A,B in SO(3) find the axis and angle of rotation of AB.
2) For a fixed A in SO(3) show that there are infinitely many pairs of planes P,Q such that A=Rp*Rq.
3) For arbitrary A,B in SO(3) find the axis and angle of rotation of AB.