# Angle between projected vectors

1. Apr 2, 2009

### emma83

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!