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Homework Help: Prove that a rotation matrix preserves distance

  1. Jun 21, 2013 #1
    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.
  2. jcsd
  3. Jun 21, 2013 #2


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    Science Advisor

    I am puzzled by the question. What, exactly, are you using as a definition of "rotation matrix". If it is the obvious- that it corresponds to a rotation- the fact that it does not change length follows immediately from the definition of "rotation".
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