Аналитическая геометрия. Часть I. Шурыгин В.В. - 8 стр.

UptoLike

ВУЗ: 

КФУ | Казань

Составители: 

Рубрика: 

M/∼
M ∼
[x] ∈ M/∼
y ∈ [x]
[x]
M
α β
2π
sin α = sin β cos α = cos β
2πk
R
α ∼ β ⇔ β −α = 2πk R/∼
S
1
= {(x, y) ∈ R
2
: x
2
+y
2
=
1} f : R/∼ 3 [α] 7→ (cos α; sin α) ∈ S
1
E
3
E
3
×E
3
∼ E
3
×E
3
V
3
= (E
3
× E
3
)/∼
a b
a A
−→
AB = a
b =
−−→
BC
−→
AB
a + b c =
−→
AC
c = a + b
A
176//= °,-|*/8b- ~80N 176//-b -+-[,6)6*8/9 /0;b-7-; M/∼ 0 ,6[b6*8K
/9 ɏ‰žŠ º’Š»Žž”Š’ ;,-|*/8b6 M .- -8,-I*,0J ~1b0b67*,8,-/80 ∼ =
P6|LM ~7*;*,8 O618-3K;,-|*/8b6 ‚176// ~1b0b67*,8,-/80ƒ [x] ∈ M/∼
-L,-[,6),- -.3*L*79*8/9 7J+; /b-0; ¡Žªž”ŒžŽ‹Ž’ y ∈ [x] = H-~8-K
;2 L79 [6L6,09 ~7*;*,86 [x] L-/868-),- 216[68? ,*1-8-3M .3*L/86b08*7?
~8-:- 176//6 · ~7*;*,8 ;,-|*/8b6 M =
    ­7*L2J}0* Lb6 .30;*36 .-16[b6J8\ 161 O618-3K;,-|*/8b6 */8*/8b*,K
,; -+36[-; .-9b79J8/9 b :*-;*8300=
    •= ¼/70 Lb6 b*}*/8b*,,N )0/76 α 0 β -870)6J8/9 ,6 )0/7-\ 1368,-*
           )                     )                       )
2π \ 8- [,6 *,09 830:-,-;*830 */10N O2,1 0M ,6 ~80N 0/76N /-b.6L6J8†
                               H
sin α = sin β \ cos α = cos β = -~8-;2 */8*/8b*,,- 36//;6830b68? 63:2;*,8
830:-,-;*830)*/10N O2,1 0M / 8-),-/8?J L- /76:6*;-:- 2πk = ¼/70 bb*/80
,6 ;,-|*/8b* b*}*/8b*,,N )0/*7 R /7*L2J}** -8,-I*,0* ~1b0b67*,8,-K
/80† α ∼ β ⇔ β − α = 2πk \ 8- O618-3K;,-|*/8b- R/∼ ;-|,- +0*180b,-
-8-+36[08? ,6 -132|,-/8? *L0,0),-:- 36L02/6 S = {(x, y) ∈ R : x +y =
                                                  1              2       2   2

1} \ .-76:69 f : R/∼ 3 [α] 7→ (cos α; sin α) ∈ S =
    ]= ˆ+-[,6)0; ;,-|*/8b- 8-)*1 :*-;*830)*/1-:- .3-/836,/8b6 /0;b-7-;
                                              1


                                 )                        )
E = „-:L6 ;,-|*/8b- :*-;*830 */10N b*18-3-b ‚2.-39L- *,,N .63 8- *1ƒ
                                                                        )
.3*L/86b79*8 /-+-M .3-0[b*L*,0* E ×E = ˆ8,-I*,0* 36b*,/8b6 :*-;*830)*K
 3


/10N b*18-3-b 9b79*8/9 -8,-I*,0*; ~1b0b67*,8,-/80 ∼ ,6 E × E = H-~8-K
                                  3       3


;2 ;,-|*/8b- /b-+-L,N b*18-3-b .3*L/86b79*8 /-+-M O618-3K;,-|*/8b-
                                                             3       3


V = (E × E )/∼ =
 3     3    3

rZÊ ËWXxÌXUx u³xTÍÎWW XÍw txyzuT͵W
ϳTxwx™xXWxZ ›œžŸ ª‘ ª” ”Š¬Šª‘Ð ”Ž‰žŠ a Œ b § ¿ž‹Š»Œ’ ”Ž‰º
žŠ a Šž Ž‰ŠžŠŠ¦ žŠ¤‰Œ A ¥ žŠ ŽžŸ ”Š¢Ÿ’Ž’ ”Ž‰žŠ −AB     →
                                                              = a ¥  ¢žŽ’
Šž‹Š»Œ’ ”Ž‰žŠ b = −BC      −→ Šž ‰ŠÑ ”Ž‰žŠ −→ § ҏ¢Š”Ž’ œ’’Š¦ ”Ž‰º
                     ª
žŠŠ” a + b ”Š¬Š ‘¦ ”Ž‰žŠ c = AC § − →
                                                   AB

    Ó*:1- .3-b*308?\ )8- b*18-3 c = a + b ,* [6b0/08 -8 b+-36 ,6)67?,-M
8-)10 A =
    ­O-3;2703-b6,,-* .36b07- /7-|*,09 /b-+-L,N b*18-3-b ,6[b6*8/9

                                      Ô

Страницы