Аналитическая геометрия. Шурыгин В.В. - 10 стр.

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a
1
=
−−→
AB
1
A
a
1
a
2
=
−−−→
B
1
B
2
a
2
a
3
=
−−−→
B
2
B
3
a
k
a
k+1
=
−−−−→
B
k
B
k+1
k = 3, 4, . . . , n −1 a
1
+
a
2
+ . . . + a
n
=
−−→
AB
n
A B
n
a
1
B
1
a
2
B
2
a
3
B
3
a
4
a
n
4
◦
a b a + x = b
x = b + (−a)
b a
x = b − a
b − a
a b a =
−→
OA
b =
−−→
OB b − a =
−→
AB
•
•
•
A
B
O
a
b
b − a
λ a
λa
1) |λa| = |λ||a| 2) λa ↑↑ a λ > 0 a 6= 0 λa ↑↓ a λ < 0 a 6= 0
· : R×V
3
→ V
3
{λ, a} 7→ λ · a = λa
5
◦
λ(a + b) = λa + λb
6
◦
(λ + µ)a = λa + µa
7
◦
(λµ)a = λ(µa)
8
◦
1 · a = a
                                        -87-|08? b*18-3 a = −AB            −→ -8 ,*1-K
                  B      3              8-3-M 8-)10 A \ [68*; -8 1-, 6 b*18-K
                                                                          1           1

                        a    4
                                        36   a   -87-|08?    b*18-3     a   =
                                                                                −−−→ \ [6K
                                                                                BB
              a  3
                                        8*; -8 1-, 6 b*18-36 a -87-|08? b*1K
                                                  1                               2       1   2


       B 1                              8-3 a = −B−−B→ 0 861 L67** === \ -8 1-,K
                                                                              2


   a1
           a 2
                 B   2
                                 a   n    6 b*18-36 a -87-|08? b*18-3 a =
                                                      3   2       3

                                        −−−−→ ‚
                                                    k = 3, 4, . . . , n − 1 ƒ\ 8-:L6 a +
                                                              k                               k+1

                                                            −−→ ­                    Æ
                                        B B
             Ç0/= Æ=                    a + . . . + a = AB = ; = 30/2,-1 =
                                              k   k+1                                             1
 A                              B    n
                                              2           n               n

   —[ /b-M/8b6 4 /7*L2*8\ )8- L79 7J+N b*1K
                     ◦
8-3-b a 0 b 236b,*,0* a + x = b 0;**8 *L0,K
/8b*,,-* 3*I*,0* x = b + (−a) \ ~8-8 b*1K A                           b−a
                                                                      •


8-3 ,6[b6*8/9 ¢ŠžŸÀ b*18-3-b b 0 a                                            B      •



0 -+-[,6)6*8/9 x = b − a = —[ .36b076 /7-K
|*,09 b*18-3-b b8*16*8 /7*L2J}** .36b07-                     a                b

L79 ,6N-|L*,09 36[,-/80 b − a † */70 -87-K                               O    •



|08? b*18-3 a 0 b -8 -L,-M 8-)10† a = −OA       →\               Ç0/= Ú =
                         −→ ­
b = OB \ 8- b − a = AB = ; = 30/2,-1 Ú =
     −−→

   ϳTxwx™xXWxZ ›ŠŒ¢”ŽªŽŒŽ’ ”Ž«Žž”ŽŠ©Š ¤Œ‹ λ Œ ”Ž‰žŠ a º
¢‘”Žž£ ”Ž‰žŠ λa ¥ ŠªŠ¢¤Š Š¡ŽªŽ‹£Ž’‘¦ ‹ŽªœÀ«Œ’Œ œ‹Š”Œ£’ŒÛ
1) |λa| = |λ||a| ¥ 2) λa ↑↑ a ¥ Ž‹Œ λ > 0 ¥ a 6= 0 ¥ Œ λa ↑↓ a ¥ Ž‹Œ λ < 0 ¥ a 6= 0 §
   ˆ8-+36|*,0*      · : R×V → V \ -8,-/9}** .63*\ /-/8-9}*M 0[ b*}*/8b*,K
,-:- )0/76 0 b*18-36\ 0N .3-0[b*L*,0*\ {λ, a} 7→ λ · a = λa \ ,6[b6*8/9
                                 3       3


Š¡ŽÑŒŽ¦ œ’Š»ŽŒ£ ”Ž‰žŠ  ¤Œ‹Š= €* 832L,- .3-b*308?\ )8- ~86
-.*36 09 -+76L6*8 /b-M/8b6;0
   5 λ(a + b) = λa + λb ‚L0/830+280b,-/8? -8,-/08*7?,- /7-|*,09 b*1K
    ◦
8-3-bā
   6 (λ + µ)a = λa + µa ‚L0/830+280b,-/8? -8,-/08*7?,- /7-|*,09 0K
    ◦                                                                                 )
/*7ā
    ◦
   7 (λµ)a = λ(µa)
   8 1 · a = a\
    ◦




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