1. The problem statement, all variables and given/known data Prove that a rotation matrix in R3 preserves distance. Such that if A is a 3*3 orthogonal rotation matrix then |A.v|=|v|. I know one can prove this is in R2 by using a trig representation of a rotation matrix and then simplifying. Is there an analogue method in R3 or some other more elegant way. A hint/push in the right direction would be nice.