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Angle between projected vectors

  1. Apr 2, 2009 #1
    1. The problem statement, all variables and given/known data
    Given two 3-vectors U and V with an angle A between them in a plane P, find the plane P' in which the angle between the 2 projected vectors U' and V' is B.
    For instance, if you consider the basis vectors X(1,0,0) and Y(0,1,0) in the plane Z=0, find the plane in which the angle between the projected vectors X' and Y' is Pi/4.


    2. Relevant equations


    3. The attempt at a solution
    I considered the example with the plane P given by x+Ay+Bz+D=0, then expressed the projections X' and Y' on it and with the condition (X'.Y')=X'.Y'.cos(Alpha) and Alpha=Pi/4 I find a complicated relation of degree 4 between A and B. I guess there is an easier way to proceed to find the equation of the plane. Thanks for your help!
     
  2. jcsd
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