Hey so, I found this and was thinking that I can help you if you can help me.

When you cross two orthonomal vectors together, you will always get another orthonormal vector (try crossing (1,0,0) and (0,1,0), which yields (0,0,1)).

Also note, that whenever a cross is performed you will always return a vector that is orthogonal (i.e. 90 degrees in between the two)to BOTH of the vectors that you crossed together.

You can prove this by doting the returned vector with the two input vectors, which will yield a 0 (Dot(a,b)=||a|| *||b|| Cos(angle between the two)) and since Cos(90) is 0, thus proved.

Sometimes you will get the 0 vector, this is technically orthogonal to every vector out there, which means that the two vectors you crossed together were similar (pointing in the same direction).

But as far as what I was wondering, I have been using this stuff in Physics, Statics, Calculus, etc and have been wondering how it can be applied to actual problems, so if you don't mind explaining why you were wanting to do this, that would be awesome :).

I have programmed for about a year and a half so I don't mind if you use programming terminoligy to explain.

Thanks :)

Petry