Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 63 стр.

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cÈÏ Ëã
67
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°ãºmÒË Ó˯ÈmËÓ°mÈ ÓãºÓºm¯ËäËÓÓº Ò°Ëã A BÒ
C
m©Ë}ÈË ÒÏ
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p
→
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q
→
Ò°ãË°mÒ«
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
{°«}ºË ¯ÈmÓËÓÒË mÒÈ
Ax By Cz D+++=
0,
ABC
++>
0
mã
º®
Ë}ȯºmº® °Ò°ËäË }ºº¯
ÒÓÈ Ë°
¯ÈmÓËÓÒË ÓË}ºº¯º® ¹ãº°
}º°Ò

iº}ÈÏÈËã°mº
s˹º°¯Ë°mËÓÓº® ¹¯ºm˯}º® ËÎÈËä°« º ¯ÈmÓËÓÒË
Ax By Cz D A B C+++= + + >00,
m°ãÈË
C≠
äºÎË© ÏȹҰÈÓº m
mÒË
det
x
DA
ABC
y
DB
ABC
z
DC
ABC
CB
CA
+
++
+
++
+
++
−
−
=
222 222 222
0
0
0

Èm°ãÈË
C=0
mmÒË
det
x
DA
AB
y
DB
AB
z
BA
+
+
+
+
+
−=
22 22
0
0
001
0

{ ººÒ² °ãÈ«² ªÒ ¯ÈmÓËÓÒ« º¹¯ËËã« ¹ãº°}º° ¹¯º²º« ˯ËÏ
ÓË}ºº¯ÏÈÈÓÓº}¹È¯ÈããËãÓºmäÓË}ºããÒÓËȯөämË}º¯Èä
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c È Ï  Ë ã                                                      67
¯«äȫҹ㺰}º°ˆ 



               °ãºmÒË Ó˯ÈmËÓ°ˆmÈ ӂã  ºÓºm¯ËäËÓÓº Ò°Ëã A B Ò C m©ˆË}Èˈ ÒÏ
                                                                                  →          →
               ÓË}ºããÒÓËȯӺ°ˆÒmË}ˆº¯ºm p Ò q Ò°ãË°ˆmÒ«
        
        
        ‘˺¯ËäȺ}ÈÏÈÓÈ
                  
                  
                  
    ‘˺¯ËäÈ                       {°«}ºË ‚¯ÈmÓËÓÒË mÒÈ Ax + By + Cz + D = 0 ,  A + B + C > 0  m ã 
    
                                   ­º® Ë}ȯˆºmº® °Ò°ˆËäË }ºº¯ÒÓȈ Ë°ˆ  ‚¯ÈmÓËÓÒË ÓË}ºˆº¯º® ¹ãº°
                                   }º°ˆÒ
                  
                  
     iº}ÈÏȈËã°ˆmº
         
         s˹º°¯Ë°ˆmËÓÓº®                                               ¹¯ºm˯}º®                              ‚­ËÎÈËä°«                                ˆº                   ‚¯ÈmÓËÓÒË
                Ax + By + Cz + D = 0 ,                                A + B + C > 0  m °ã‚ÈË C≠ äºÎˈ ­©ˆ  ÏȹҰÈÓº m
               mÒË
               
               
                                                             DA                                       DB                                      DC
                                                  x+                                       y+                                      z+
                                                          A + B2 + C2
                                                              2
                                                                                                   A + B2 + C2
                                                                                                      2
                                                                                                                                           A + B2 + C2
                                                                                                                                              2


                                       det                        0                                       −C                                       B                      = 0 

                                                                  C                                        0                                      −A
                                                                                                             
                                                                                                             
               Èm°ã‚ÈËC=0mmÒË
               
               
                                                                                  DA                               DB
                                                                       x+                              y+                              z+0
                                                                                A + B2
                                                                                   2
                                                                                                                 A + B2
                                                                                                                   2


                                                             det               −B                                  A                      0         = 0 

                                                                                  0                                0                      1
           
           
           { º­ºÒ² °ã‚È«² ªˆÒ ‚¯ÈmÓËÓÒ« º¹¯ËËã« ˆ ¹ãº°}º°ˆ  ¹¯º²º«‚  ˯ËÏ
           ÓË}ºˆº¯‚ ÏÈÈÓӂ ˆº}‚¹È¯ÈããËã Óºm‚äÓË}ºããÒÓËȯөämË}ˆº¯Èä
           
           
        ‘˺¯ËäȺ}ÈÏÈÓÈ
             
             

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