Аналитическая геометрия. Часть I. Шурыгин В.В. - 27 стр.

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3
R
3
W
m
⊂ V
n
V
n
n
A
n
m (m ) A
n
(0 6 m 6 n)
A
W
m
A
n
π
m
= {M ∈ A
n
|
−−→
AM ∈ W
m
}.
(π
m
, W
m
, ψ|
π
) ψ|
π
ψ π
m
×π
m
m
A
n
AB BC CA
ABC C
0
A
0
B
0
(BCA
0
) = λ
1
(CAB
0
) = λ
2
(ABC
0
) = λ
3
A
0
B
0
C
0
λ
1
λ
2
λ
3
= −1
{O, e
i
}
O = A e
1
=
−→
AB e
2
=
−→
AC
)6/8,-/80\ b/* 6OO0,,* .3-/836,/8b6 36[;*3,-/80 3 0[-;-3O, :*-;*8K
30)*/1-;2 .3-/836,/8b2 0 6OO0,,-;2 .3-/836,/8b2 R =                   3
   ð͵xñÍXWxZ H-/3*L/8b-; bb*L*,09 6OO0,,N .3-/836,/8b ; .-72)6*;
b-[;-|,-/8? ,* 8-7?1- /83-:- -.0/68? :*-;*830)*/1-* 83*N;*3,-* .3-/8K
36,/8b- 0 :*-;*830)*/12J .7-/1-/8?\ ,- 0 36//;6830b68? 0N ;,-:-;*3,*
6,67-:0= ˆ8;*80;\ )8- -/86*8/9 *}* -.3*L*708? 8610* :*-;*830)*/10* .-K
,9809 161 36//8-9,0* ;*|L2 8-)16;0 0 2:-7 ;*|L2 .39;;0= “8- +2L*8
-/2}*/8b7*,- ,0|* / .-;-}?J -.*36 00 /16793,-:- .3-0[b*L*,09 b*18-K
3-b=
   ϳTxwx™xXWxZ ›œžŸ W ⊂ V ¡Šª¡Šžž”Š ” ”Ž‰žŠŠ’ ¡Šº
žž”Ž V ¥ ŠÑŒŒŠ”Š’  n º’Ž‘’ ÉɌ‘’ ¡Šžž”Š’
                              m           n


A § ›‹Š‰ŠžŸÀ ¢’ŽŠžŒ m (m º¡‹Š‰ŠžŸÀ) ” A (0 6 m 6 n) ¥
                 n


¡ŠÐŠª£«Ž¦ ¤ŽŽ¢ žŠ¤‰œ A Œ Œ’ŽÀ«Ž¦     ¡”‹£À«ŽŽ ”Ž‰žŠŠŽ ¡Šª¡Šº
 n                                                                        n


žž”Š W ¥ ¢‘”Žž£ ‹ŽªœÀ«ŽŽ ¡Šª’Š»Žž”Š ” A †
                 m                                                            n

                                        −−→
                         πm = {M ∈ An | AM ∈ Wm }.
   { :*-;*830)*/1-; .3-/836,/8b* •K.7-/1-/80 · ~8- .39;*\6 ]K.7-/1-/80
· ~8-  -+),* .7-/1-/80=
   —[ ~8-:- -.3*L*7*,09 /7*L2*8\ )8- 83-M16 (π , W , ψ| ) \ :L* ψ| · -:36K
,0)*,0* -8-+36|*,09 ψ ,6 π × π \ · mK;*3,-* 6OO0,,-* .3-/836,/8b- =
                                                      m           m       π       π


„61-* .3-/836,/8b- ,6[b6*8/9 ¡Šª¡Šžž”Š’ b A =
                                  m       m

                                                                      n

ÊZ ˜TWµxTUZ
­7*L2J}0* .30;*3 .-16[b6J8\ 161 6OO0,,* 1--3L0,68 0 .3-/8-*
-8,-I*,0* 83*N 8-)*1 ;-:28 0/.-7?[-b68?/9 .30 3*I*,00 :*-;*830)*/10N
[6L6)=
   ðÍwÍñÍ Z ‚„*-3*;6 °*,*769ƒ= €6 /8-3-,6N AB \ BC 0 CA 83*2:-7?,016
              )                        )
ABC L6, 8- 10 C \ A 0 B 8610*\ 8- (BCA ) = λ \ (CAB ) = λ 0
               ‡          ) )
(ABC ) = λ = -16[68?\ 8- 8- 10 A \ B 0 C 7*|68 ,6 -L,-M .39;-M
                     0    0           0                       0       1           0       2


8-:L6 0 8-7?1- 8-:L6\ 1-:L6 λ λ λ = −1 =
     0       3                                0   0       0


   àxÿxXWxZ ­;= 30/2,-1 •Ú = Ç6//;-830; 6OO0,,M 3*.*3 {O, e } \ :L*
                                  1 2 3


                        −→ {
O = A \ e = AB \ e = AC = ~8-; 3*.*3* b*3I0, 83*2:-7?,016 0 36/K
                                                                                      i
              −→
         1           2
                                    ïÈ

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