Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 65 стр.

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cÈÏ Ëã
69
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c È Ï  Ë ã                                                      69
¯«äȫҹ㺰}º°ˆ 



                                                                           n x ( x − x0 ) + n y ( y − y0 ) + nz ( z − z0 ) = 0 
                        
                                 ÒãÒ º­ºÏÓÈÈ« A = n x ;                                  B = n y ; C = n z ; D = − n x x 0 − n y y 0 − n z z 0  ¹ºã‚
                                 Òä Ax + By + Cz + D = 0 
                        
                        
                        
    vãË°ˆmÒË                     p°ãÒ ¹ãº°}º°ˆ  ÏÈÈÓÈ m º¯ˆºÓº¯äÒ¯ºmÈÓÓº® °Ò°ˆËäË }ºº¯ÒÓȈ
                                     →     →      →
                                    {O, e1 , e2 , e3 } ‚¯ÈmÓËÓÒËä Ax + By + Cz + D = 0 Ë A + B + C > 0 ˆº
                                               A
                                                      →
                                   mË}ˆº¯ n = B º¯ˆººÓÈãËÓªˆº®¹ãº°}º°ˆÒ
                                               C
                        
                        
                        
                                                    →                                                                                                                 →       → →
    |¹¯ËËãËÓÒË                   {Ë}ˆº¯ n ÓÈÏ©mÈˈ°«tvéujst€uknrzvévu¹ãº°}º°ˆÒ ( r − r0 , n ) = 0 
    
                        
                                                                A
    
    |¹¯ËËãËÓÒË                   {Ë}ˆº¯                       B               ÓÈÏ©mÈˈ°«                          msjkt€u                     knrzvévu                        ¹ãº°}º°ˆÒ
    
                                                                 C
                                    Ax + By + Cz + D = 0 ,                                A + B + C > 0 
         
         
       {º¯ˆºÓº¯äÒ¯ºmÈÓÓº®°Ò°ˆËäË}ºº¯ÒÓȈãÈmÓ©®mË}ˆº¯¹ãº°}º°ˆÒ«mã«Ëˆ°«Ò
Óº¯äÈã Ó©äËËmË}ˆº¯ºä
         
         
                                                                                                  →      →      →
    ~ÈÈÈ                        Æ xqxznun rvvélqtjz {O, g1 , g 2 , g 3 }  tjpzq éjxxzv¹tqn vz zv·rq M x
    
                                                                             →
                                                                                          x∗
                                                                                                                                       →      → →
                                   éjlqyxknrzvévu r = y ∗ lvwsvxrvxzq ( r − r0 , n ) = 0 
                                                                              ∗

                                                                                          z∗
                        
    cËËÓÒË                      ° ‚°ˆ  K Ë°ˆ  º¯ˆººÓÈã ÓÈ« ¹¯ºË}Ò« ˆº}Ò M ÓÈ ÈÓӂ  ¹ãº°
                                                                             →              →            →        →           →
                                         }º°ˆ ˆºÈ MK = λ n Ò r = r ∗ + λ n  vä¯Ò° 
                                             
                                             
                                   ° ‘º}È K¹¯ÒÓÈãËÎ҈ÈÓÓº®¹ãº°}º°ˆÒ¹ºªˆºä‚ÒäËˈäË°ˆº°º
                                                                           → →               →      →
                                             ºˆÓº ËÓÒË ( n , r ∗ + λ n − r0 ) = 0 
                        
                        
                        

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