Аналитическая геометрия и линейная алгебра. Умнов А.Е. - 31 стр.

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cÈÏ Ëã
35
{Ë}º¯©ÒãÒÓˮөËº¹Ë¯ÈÒÒ°ÓÒäÒ

M
N

g
3
→

g
2
→

O

g
1
→
èqxytvr
ÒÓÈmË}º¯ºm
°
3
2
1
ξ
ξ
ξ
=
→
OM
Ò
3
2
1
η
η
η
=
→
ON
ºÈ
OM MN ON MN ON OM
→→ → → →→
+= =−
;
Òº}ºÓÈËãÓº
33
22
11
ξη
ξη
ξη
−
−
−
=
→
MN

~ÈÈÈ

Ætnrvzvévpvinplnrjézvkvpxqxznunrvvélqtjz
{, , , }Og g g
123
→→ →
ojlj
trvvélqtjztnxvkwjljíq}zv·nr
M
1
q
M
2
ls¹rvzvé}xvvzknz
xzknttv
3
2
1
1
ξ
ξ
ξ
=
→
OM
q
3
2
1
2
η
η
η
=
→
OM

Òéniynzx¹tjpzqzv·ry
M
zjryí·zv
MM MM
12
→→
=
λ

cËËÓÒË
~ÈäËÒäº
λ
äºÎË¹¯ÒÓÒäÈãºËÏÓÈËÓÒË}¯ºäË
¹¯Ò}ºº¯ºäº}È
M
²ºÒmË°}ºÓËÓº° cÒ°  sÈ®Ëä ¯ÈÒ°mË}º¯ º}Ò
M
 jÏ
°ººÓºËÓÒ®m¯ËºãÓÒ}Ȳ
MOM
1
Ò
2
OMM
¹ºãÈËä
OM M M OM OM MM OM
11 2 2
→→→ →→ →
+= +=
;

1
M
M

2
M
O
èqxytvr
ÓºÈ}}È}
MM MM
12
→→
=
λ
º
OM OM OM OM
→→ →→
−= −
12
λ
()
Òº}ºÓÈËãÓº
→→→
+
+
+
=
21
11
1
OMOMOM
λ
λ
λ

c È Ï  Ë ã                                                      35
{Ë}ˆº¯©ÒãÒÓˮө˺¹Ë¯ÈÒÒ°ÓÒäÒ



                                                                                    ÒÓȈmË}ˆº¯ºm
                                                                                    
    M                                                             ξ1           η1
                                                                                                        → →
    
                                                                                     ‚°ˆ  OM = ξ 2 Ò ON = η 2 ‘ºÈ
    N
                 →                                                                               ξ3           η3
     g3                                                                                           →            →             →                  →             →            →
                                                         →                                              OM + MN = ON                            ;       MN = ON − OM 
     g2                                             
    O                                                                          Òº}ºÓȈËã Óº
    
    
                                                                                                                                      η1 − ξ1
                                                                                                                                  →
                          →                                                                                                      MN = η 2 − ξ 2 
     g1 
                                                                                                                                     η3 − ξ 3
    èqxytvr
              
              
              
                                                                                                                                                                        →      →       →
    ~ÈÈÈ                        Ætnrvzvévpvinplnrjézvkvpxqxznunrvvélqtjz {O, g1 , g 2 , g 3 } ojlj
    
                                   t€rvvélqtjz€tnxvkwjljíq}zv·nr M1 qM2 ls¹rvzvé€}xvvzknz
                                   xzknttv
                                                                                              ξ1                 η1
                                                                                          →                →
                                                                                       OM 1 = ξ 2 q OM 2 = η 2 
                                                                                              ξ3                 η3
                                                                                                                                    →                     →
                                   Òéniynzx¹tjpzqzv·ryMzjryí·zv M 1 M = λ MM 2 
                  
    cËËÓÒË
    
            ~ÈäˈÒ䈺 λäºÎˈ¹¯ÒÓÒäȈ ã ­ºËÏÓÈËÓÒË}¯ºäË ¹¯Ò}ºˆº¯ºäˆº}È
            M ‚²º҈ m ­Ë°}ºÓËÓº°ˆ  cÒ°   sÈ®Ëä ¯È҂°mË}ˆº¯ ˆº}Ò M jÏ
            °ººˆÓº ËÓÒ®mˆ¯Ë‚ºã ÓÒ}Ȳ OM 1 M Ò OMM 2 ¹ºã‚ÈËä
                                                                →               →               →                   →             →                 →
                                                             OM 1 + M 1 M = OM                            ; OM + MM 2 = OM 2 
                  
                                                                                                                             →                      →
     M 1 
                                                                                            ÓºˆÈ}}È} M 1 M = λ MM 2 ˆº
    
                                                                                            
    M                                                        
                                                                                                                        →             →                      →            →
     M 2                                                                      OM − OM 1 = λ (OM 2 − OM ) 
                                                                                                                                                    
     O                                                                                                                                              
    
                                                                                                                                      →                →     λ    →
                                                                                                                                                 1
                                                                                            Òº}ºÓȈËã Óº OM =                                     OM1 +      OM 2 
                                                                                                                                                1+ λ       1+ λ
    èqxytvr
    

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