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Math Help - Prove: Counterclockwise and positive determinant

  1. #1
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    Prove: Counterclockwise and positive determinant

    Hi,

    I'm trying to prove fact, that positive determinant of e.g Prove: Counterclockwise and positive determinant-determinant_5.gif 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
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  2. #2
    MHF Contributor

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    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.
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