Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 48 стр.

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                                                                             →    →       →                             →       →     →
            ‚°ˆ  ÏÈÈÓÈ °Ò°ˆËäÈ }ºº¯ÒÓȈ {O, g1 , g 2 , g 3 }  Ò ˆ¯Ò mË}ˆº¯È a  b  Ò c  ã«
                →         →            →     →     →         →          →         →           →       →         →           →
}ºˆº¯©² a = ξ1 g1 + ξ2 g 2 + ξ3 g 3  b = η1 g1 + η2 g 2 + η3 g 3 Ò c = κ 1 g1 + κ 2 g 2 + κ 3 g 3 
       
       
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                                       →→         ξ2 ξ3 →         ξ ξ3 →          ξ ξ2 →
                                   [a, b ]= det          f1 − det 1     f 2 + det 1      f ,
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                      →       →    →
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                                                                    → → →   →       →
                                                                      ( g , g , g ) , k = j  ¹ºªˆºä‚ã«
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                                                                     0 ,            k≠ j
 → → →
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                     → →→                    ξ2 ξ3           ξ1 ξ3           ξ1 ξ2                             →    →   →
                                   (
                    (a , b, c ) = κ 1 det
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                                                   − κ 2 det
                                                             η1 η3
                                                                   + κ 3 det
                                                                             η1 η2                        )( g , g , g ) =
                                                                                                                1   2       3


                                        ξ1 ξ2 ξ3                                                                                
                                                   → → →
                                  = det η1 η2 η3 ( g1 , g2 , g3 )            ,
                                        κ1 κ 2 κ 3
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                                                                      ξ1 ξ2 ξ3
                                                           →→→
                                   mˆÈ}ºä­ÈÏÒ°Ë ( a , b, c ) = det η1 η2 η3                         .
                                                                      κ1 κ 2 κ 3
                                                                                          →   →   →
                          °iã«mmËËÓÓ©²m¹mË}ˆº¯ºm f 1 , f 2 , f 3 °¹¯ÈmËãÒmÈ