Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 77 стр.

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c È Ï  Ë ã                                                      81
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                                                                                                              →                              →       →        →
    ~ÈÈÈ                        bjt€zv·rjxéjlqyxknrzvévu R qwé¹uj¹ r = r0 + τ a Ëjpzqéjxxzv¹
    
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                                   mvwévqoknlntq¹

    
    cËËÓÒË                                                                                                      ° ¯ºmËËä ˯ËÏ ÈÓӂ  ˆº}‚ °
                                                              →                                                                                                             →
     D                                                                                 ¯È҂°mË}ˆº¯ºä R  ¹ãº°}º°ˆ 
                                                                                                                           ¹Ë¯¹ËÓÒ}‚㫯ӂ ¹¯«äº® cÒ°
                                                                                                                                                                                        →
    
                                                                                                                            |­ºÏÓÈÒä˯ËÏ rx ¯ÈÒ
                                                                          →                                                 ‚°mË}ˆº¯ ˆº}Ò ¹Ë¯Ë°ËËÓÒ«
     R                                                                          ¹¯«äº®Ò¹ãº°}º°ˆÒ‘ºÈÒ°}º
                                                             →
                                                                                                                            äºË ¯È°°ˆº«ÓÒË ­‚ˈ ¯ÈmÓº
     rx                                                                                               →       →
                                                                                                                             ρ = | R − rx | 
                                    →
                                                                                                                   
     r0                                                                                                                      →
    O                                                            ° ‘º}È rx  ­‚ˈ ‚ºmãˈmº¯«ˆ 
                                                                                                                        ºÓºm¯ËäËÓÓº      °ººˆÓº ËÓÒ«ä
                                                                                                                              → →            →                         →         →             →
                                                                                                                           ( a , R − rx ) = 0  Ò rx = r0 + λ a  Óº
    èqxytvr                                                                                           ˆºÈÒ°}ã È«¹È¯Èäˈ¯ λ 
                                                                                                                                                                                    →       → →
                                                                                                          ( R − r0 , a ) →                                    →         →
        ÓȲºÒ䈺 rx = r0 +      →         a
                                                                                                                   2
                                                                                                              |a |
                                                                                                       
                                                         →       → →                                  →        → →                                                     →     → →
                                    ( R − r0 , a ) → → → ( R − r0 , a ) →
                                       →       →                                                                                                  →    →           ( R − r0 , a ) 2
                Ò ρ = ( R − r0 −      →
                                                   a , R − r0 −  →
                                                                        a) =                                                                  | R − r0 |2 −                 →
                                                                                                                                                                                                
                                             2                       2                                                                                                            2
                                        |a |                    |a |                                                                                                       |a |
                                                                                                       
                                                                                                                             → 2 → 2                   → →                    → →           2
    ~ÈäˈÒ䈺m°Òã‚ãË}º¹¯ºm˯«Ë人ˆºÎ˰ˆmÈ p                                                                                 q         = ( p , q ) + [ p , q ] ÈÓ
                                                                                                                                                                   2


                                                                                                                                                                    →       → →
                                                                                                                                                                  [ R − r0 , a ]
    ÓºË¯Ë ËÓÒ˰ºm¹ÈÈˈ°¹ºã‚ËÓÓ©äm}ºÓ˹ÏÓÈËÓÒËä ρ =                                                                                                        →
                                                                                                                                                                                            
                                                                                                                                                                           |a|
                  
                  
                  
                                                                                                                       →        →            →           →        →            →
    ~ÈÈÈ                        Ëjpzqéjxxzv¹tqnun lywé¹u€uq r = r01 + τ a1 q r = r02 + τ a 2 
    
                  
                                                                      →            →
    cËËÓÒË                °p°ãÒmË}ˆº¯© a1 Ò a 2 }ºããÒÓËȯөˆº¯Ë ËÓÒ˰ãË‚ˈÒϯҰÒ
                                                                                                           →           →    →
                                                                                         S            |[r02 − r01 , a1 ]|
                                    Èˈ°«Áº¯ä‚㺮 ρ =                                 →
                                                                                                =                  →
                                                                                                                                     
                                                                                      | a1 |                    | a1 |