Аналитическая геометрия. Шурыгин В.В. - 25 стр.

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E AB (ABE) = 1
r
E
=
r
A
+ r
B
2
, x
i
E
=
x
i
A
+ x
i
B
2
, i = 1, 2, 3.
(A, V, ψ)
A
V ψ : A×A → V
{A, B} A
V
−→
AB
1
◦
A ∈ A v ∈ V B
−→
AB = v
2
◦
−→
AB+
−−→
BC =
−→
AC
A, B, C ∈ A ( )
A
V
A dim A A
V
n A
n
−→
AA = 0
−→
AB = −
−→
BA
2
◦
B = C = A C = A
(V, V, ψ) ψ : {a, b} 7→ b − a V =
R
n
R
n
n
n
     ¼/70 8-)16 E 9b79*8/9 /*3*L0,-M -83*[16 AB \ 8- (ABE) = 1 0
                     rA + rB             xiA + xiB
                rE =         ,   xiE   =           ,   i = 1, 2, 3.
                        2                    2
ÊZÊ         WXXux ³Tu¶zTÍX¶ztu
­O-3;2703-b6,,-* bI* .-,980* b*18-3,-:- .3-/836,/8b6 .-[b-79*8 /
.-;-}?J .3-/8-:- /.0/16 61/0-; .-7,-/8?J -.0/68? /b-M/8b6 /b-+-L,N
b*18-3-b :*-;*830)*/1-:- .3-/836,/8b6= ­7*L2J}** ,0|* -.3*L*7*,0* 6OK
O0,,-:- .3-/836,/8b6 .-[b-79*8 61/0-;680)*/10 [6L68? /6;- :*-;*830)*K
/1-* .3-/836,/8b- 161 ;,-|*/8b- 8-)*1=
    ϳTxwx™xXWxZ ÉɌ‘’ ¡Šžž”Š’ ¢‘”Žž£ žŠ¦‰ (A, V, ψ) ¥
ŠžŠ£«£ Œ¢ Ž‰ŠžŠŠ©Š ’Š»Žž” A ¥ ˎ’Žž‘ ‰ŠžŠŠ©Š ¢‘”Àžº
£ žŠ¤‰’Œ¥ ”Ž‰žŠŠ©Š ¡Šžž” V Œ ŠžŠ¬»ŽŒ£ ψ : A×A → V ¥
ŠžŠ£«Ž©Š œ¡Š£ªŠ¤ŽŠ¦ ¡Ž žŠ¤Ž‰ {A, B} ’Š»Žž” A Ž‰ŠžŠ‘¦
”Ž‰žŠ Œ¢ V ¥ Š¬Š¢¤Ž’‘¦ −AB → ž‰Š©Š ¤žŠ ”‘ Š‹£Àž£ ‹ŽªœÀ«ŒŽ
ª”Ž ‰ŒŠ’‘†                     ¥        ¥        ¡
                                                   ª
   1 ö‹£ ‹À¬‘Ð A ∈ A Œ v ∈ V œ«Žž”œŽž Ž Œž”Ž£ žŠ¤‰ B
     ◦
ž‰£¥ ¤žŠ −AB →
                  = v§
       −→ −−→ −→ ª
   2 AB+ BC = AC ‹£ ‹À¬‘Ð A, B, C ∈ A (”Žž”Š žŽœ©Š‹ŸŒ‰) =
     ◦
   5OO0,,-* .3-/836,/8b- -+),- -+-[,6)6*8/9 -L,0; /0;b-7-; A = {*1K
8-3,-* .3-/836,/8b- V ,6[b6*8/9 ŠÑŒŒŠ”‘’ / 6OO0,,; .3-K
/836,/8b-; A = ¢’ŽŠžŸÀ dim A 6OO0,,-:- .3-/836,/8b6 A ,6[b6*8K
/9 36[;*3,-/8? 6//- 003-b6,,-:- b*18-3,-:- .3-/836,/8b6 V = 5OO0,,-*
.3-/836,/8b- 36[;*3,-/80 n +2L*; -+-[,6)68? /7*L2J}0; -+36[-;† A =
    —[ -.3*L*7*,09 6OO0,,-:- .3-/836,/8b6 7*:1- bb-L98/9 /7*L2J}0*   n


Lb6 /--8,-I*,09†
    •ƒ −AA
         →
            = 0 Å ]ƒ AB = −BA =
                     −→      −→
   ‡79 0N L-16[68*7?/8b6 L-/868-),- [6.0/68? 36b*,/8b- 83*2:-7?,016 2
/,6)676 .30 B = C = A \ 6 [68*; .30 C = A =
                                                                          ◦


    ­ 16|L; b*18-3,; .3-/836,/8b-; ;-|,- 6//- 003-b68? 6OO0,,-*
.3-/836,/8b- (V, V, ψ) \ .-76:69 ψ : {a, b} 7→ b − a = H-76:69 [68*; V =
 n        )
R \.-72 0; 4/86,L638,-*< 6OO0,,-* .3-/836,/8b- R 36[;*3,-/80 n L79
                                                             n
16|L-:- n =
                                    ï¾

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