Maths: Determining angle in 3D space

Posted by 742 on Stack Overflow See other posts from Stack Overflow or by 742
Published on 2010-06-17T19:44:38Z Indexed on 2010/06/17 19:53 UTC
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math

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3dgraphics

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euler-angles

I hope this is the proper location to ask this question which is the same as this one, but expressed as pure math instead of graphically (at least I hope I translated the problem to math correctly).

Considering:

two vectors that are orthogonal: Up (ux, uy, uz) and Look (lx, ly, lz)
a plane P which is perpendicular to Look (hence including Up)
Y1 which is the projection of Y (vertical axis) along Look onto P

Question: what is the value of the angle between Y1 and Up?

As mathematicians will agree, this is a very basic question, but I've been scratching my head on walls now for at least two weeks without being able to visualize the solution... maybe now too old for finding solutions to school exercises.

I'm looking for the scalar trigonometric solution, not a solution using a matrix. Thanks.

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