Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 66 стр.

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λ
=−
−
→
∗
→
→
→
(, )
||
nr r
n
0
2
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ÓÒ«¹ºãÒä
|||( ,
||
)|.
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n
n
→
∗
→
→
→
→
=−
0
°
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º¯
n
A
B
C
→
=
Ë Óº¯äÈã
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.0
=+++ DCzByAx
M

n
→

λ
n
→

r
0
→

r
∗
→
K

r
→
O
èqxytvr
ºªºä
||
|( ) ( ) ( )|
MK
Ax x By y Cz z
ABC
→
∗∗∗
=
−+ −+ −
++
000
222
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mÓÒäÈÓÒË º º}È
r
0
→
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Ax By Cz D
000
0+++=
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ABC
++>
0
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¹Ò°ÈmmÒË
||
||
MK
Ax By Cz D
ABC
→
∗∗∗
=
+++
++
222

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1111
0+++=,
ABC
111
0
++>
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2222
0
+++=
,
ABC
222
0
++>
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λ
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Ax By Cz D
Ax By Cz D
1111
2222
0
0
+++=
+++=
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ÙkÓÈã҈ÒË°}È«˺äˈ¯Ò«ÒãÒÓË®ÓÈ«ÈãË­¯ÈµäÓºmkp



                 Ò°ã˺mȈËã Óº                           M
                                          → →            →                                  →
                                         ( n , r ∗ − r0 )                   n 
                                λ=−              →2
                                                                         
                                                                                                                       →
                                                | n|                        λ n 
                     ˆºÈã«Ò°}ºäºº¯È°°ˆº«                      →           →
                     ÓÒ«¹ºã‚Òä                r0  r ∗ 
                                                          →
                                →          →      →       n                K
                                            ∗
                             | MK | = |( r − r0 ,         →   )|.                                               →
                                                    r 
                                              |n|  
                   °cÈ°°äºˆ¯Òä ˆË¹Ë¯  vézv 
                      tvéuqévkjttyí °Ò°ˆËä‚ }º 
                      º¯ÒÓȈ{ªˆºä°ã‚ÈËmË}           O
                                 A                 
                            →                      
                      ˆº¯ n = B  ­‚ˈ Óº¯äÈã  
                                 C                                      èqxytvr
                      Ó©ä mË}ˆº¯ºä ¹ãº°}º°ˆÒ
                       Ax + By + Cz + D = 0 . 
                   
                                         →             | A( x ∗ − x 0 ) + B( y ∗ − y 0 ) + C ( z ∗ − z 0 ) |
                     ºªˆºä‚ | MK | =                                                                          Óº ¹¯ÒÓÒäÈ« mº
                                                                         A2 + B 2 + C 2
                                                                   →
                     mÓÒäÈÓÒË ˆº ˆº}È r0  ¹¯ÒÓÈãËÎ҈ ÈÓÓº® ¹ãº°}º°ˆÒ ˆº Ë°ˆ 
                      Ax 0 + By 0 + Cz 0 + D = 0 Òˆº A + B + C > 0 ºˆmˈÏÈÈÒäºÎÓºÏÈ
                     ¹Ò°Èˆ mmÒË
               
                                                              →        | Ax ∗ + By ∗ + Cz ∗ + D |
                                                          | MK | =                                     
                                                                             A2 + B 2 + C 2



    ‘˺¯ËäÈ             ãº°}º°ˆÒ                      A1 x + B1 y + C1 z + D1 = 0 ,                 A1 + B1 + C1 > 0                     Ò
    
                          A2 x + B2 y + C2 z + D2 = 0 ,                 A2 + B2 + C2 > 0  ¹È¯ÈããËã Ó© ˆºÈ Ò
                         ˆºã }ºˆºÈ}ºÈÒ²ãÈmÓ©ËmË}ˆº¯©}ºããÒÓËȯө


     iº}ÈÏȈËã°ˆmº
      
         iº}ÈÎË亰ˆÈˆºÓº°ˆ p°ãÒãÈmÓ©ËmË}ˆº¯©}ºããÒÓËȯөˆº°‚Ë°ˆm‚ˈˆÈ
         }ºËÒ°ãºλ≠0ˆº A1 = λ A2 ; B1 = λ B2 ; C1 = λ C2 Ò°Ò°ˆËäÈ‚¯ÈmÓËÓÒ®
          
                                                               A1 x + B1 y + C1 z + D1 = 0
                                                                                           
                                                               A2 x + B2 y + C2 z + D2 = 0
                                                                                

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