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Prove: Counterclockwise and positive determinant

Hi,

I'm trying to prove fact, that positive determinant of e.g Attachment 28304 is counter-clockwise then and only then when the determinant is positive. In other words, that (u,v,p), where u=(a,d,g); v=(b,e,h), p=(c,f,i); is right-oriented set in R3.

I tried to play with matrix of rotation, but I wasn't successful.

Thank for ideas

P.S I'm not sure about the right English terminology, sorry for that

Re: Prove: Counterclockwise and positive determinant

So you want to prove **what** is "counter-clockwise" if and only if the determinant is positive? You mean, I think, that the matrix maps a "right hand basis" into a right hand basis if and only if the determinant is positive.

One way to do that is use the fact that the **signed** volume of the tetradhedron bounded by vectors u, v, w is the determinant having those vectors as columns.