Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 47 стр.

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cÈÏ Ëã
51
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( a
b
c
)
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(,,) |[,]|
[,]
abc ab c
ab
→→→ →→
=
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ý
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
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 b
 a
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S = |
[ a
, b
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¹º°¯ºËÓÓºº ÓÈ mË}º¯È²
a
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b
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ab
cc
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α
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S
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(,,)

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α
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= cbacba
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°
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→→→ →→→ →→→ →→→ →→→ →→→
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c È Ï  Ë ã                                                      51
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                                                                                                                                                                                 →         →
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                                    →
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                                                           →       →       →
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                                                       →
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                                                                               → → →                 → →                             →
                                                                             ( a , b , c ) = | [ a , b ] | ý → → c 
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                                                                                                              → →
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                                                                                                 [ a ,b ]
        
                                                                                      °º°ÓºmÈÓÒËäSºˆ}‚È °ä¯Ò° 
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                              →
         a                                                                                             ( a , b , c ) = | [ a , b ] | | c | cos α 
                                                                                      ˆº Ò ¹ºÏmºã«Ëˆ °ËãȈ  ÏÈ}ã ËÓÒË º ÏÓÈ}Ë
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                                           → → →                    → → →                   → → →                       → → →                      → → →                       → → →
                                 ° ( a , b , c ) = ( c , a , b ) = ( b , c , a ) = − ( b , a , c ) = − ( c , b , a ) = − ( a , c , b ) 
                                 
                                               → → →                       → → →
                                 ° ( λ a , b , c ) = λ ( a , b , c ) 
                                 
                                            →         → → →                     → → →                       → → →
                                 ° ( a 1 + a 2 , b , c ) = ( a 1 , b , c ) + ( a 2 , b , c ) 
        
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