Аналитическая геометрия. Часть I. Шурыгин В.В. - 9 стр.

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−→
AB +
−−→
BC =
−→
AC.
+ : V
3
× V
3
→ V
3
{a, b} 7→ a + b
1
◦
a + b = b + a
2
◦
(a + b) + c = a + (b + c)
3
◦
0
a a + 0 = a
4
◦
a b a + b = 0
b = −a a
1
◦
2
◦
O
b
B
A
C
a
a
b
a + b =
−→
OC OACB
−→
OA = a
−−→
OB = b
0 −a
a a =
−→
AB
−a =
−→
BA
2
◦
n
a
1
+ a
2
+ . . . + a
n
a
1
+a
2
+
. . .+a
n
¡”Œ‹Š’ žŽœ©Š‹ŸŒ‰= ˆ,- b36|6*8/9 /7*L2J}*M O-3;27-M†
                             −→ −−→ −→
                             AB + BC = AC.

   ˆ8-+36|*,0* + : V × V → V \ -8,-/9}** .63* /b-+-L,N b*18-3-b
0N /2;;2\ {a, b} 7→ a + b \ ,6[b6*8/9 Š¡ŽÑŒŽ¦ ‹Š»ŽŒ£ ”Ž‰žŠŠ”= “86
                       3     3       3


-.*36 09 -+76L6*8 /7*L2J}0;0 /b-M/8b6;0†
   1 a + b = b + a ‚1-;;28680b,-/8?ƒ Å
     ◦

   2 (a + b) + c = a + (b + c) ‚6//- 0680b,-/8?ƒ Å
                                                                )
     ◦

   3 /2}*/8b2*8 b*18-3 0 \ ,6[b6*;M œ‹Ž”‘’ ”Ž‰žŠŠ’\ 861-M\ 8- L79
     ◦
7J+-:- b*18-36 a b.-7,9*8/9 a + 0 = a Å
                                                        )
   4 L79 7J+-:- b*18-36 a /2}*/8b2*8 b*18-3 b 861-M\ 8- a + b = 0 \
~8-8 b*18-3 -+-[,6)6*8/9 b = −a 0 ,6[b6*8/9 ¡ŠžŒ”Š¡Š‹Š»‘’ ‰ a
     ◦



”Ž‰žŠŠ’§
   ‡-16[68*7?/8b6 /b-M/8b 1 0 2 -)*b0L, 0[ /7*L2J}0N 30/2,1-b • 0 ]†
                            ◦    ◦


              B                                      Ö
                      a
                                                           ØÖ
        b                    C
                                                         Õ        ×
                                                            ÖØ×
   O                   b              Õ
             a
                 A
               Ç0/= •=                              Ç0/= ]=
      —[ 30/2,16 • 7*:1- 2/;6830b6*8/9 ¡”Œ‹Š ¡‹‹Ž‹Š©’’ L79 /7-|*K
,09 b*18-3-b† /2;;6 a + b = −OC → L06:-,67? .63677*7-:36;;6
                                   ·                              OACB /-
/8-3-,6;0 −OA  →
                 = a 0 OB = b =
                        −−→
      {*18-3 0 · ~8- 176// ,27*bN b*18-3-b\ 6 b*18-3 −a 0;**8 82 |* L70,2\
)8- 0 b*18-3 a \ 0 .3-80b-.-7-|,-* ,6.36b7*,0*\ 8- */8?\ */70 a = −AB → \ 8-

−a = BA =
         −→
      —[ /b-M/8b6 2 /7*L2*8\ )8- 3*[27?868 b)0/7*,09 /2;; n b*18-3-b
                 ◦

a + a + . . . + a ,* [6b0/08 -8 36//86,-b10 /1-+-1 ‚.- -.3*L*7*,0J ;
;-|*; /176Lb68? 8-7?1- Lb6 b*18-36®ƒ\ 0 L79 ,6N-|L*,09 /2;; a +a +
 1       2       n


. . . + a ;-|,- b-/.-7?[-b68?/9 /7*L2J}0; ¡”Œ‹Š’ ¢’‘‰Œ£ ‹Š’Š¦†
                                                                    1    2

         n

                                      Ù

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