Аналитическая геометрия. Шурыгин В.В. - 47 стр.

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M
0
(R; 0)
A
ω ` t = ∠M
0
OA
−→
OA = R e(t)
|
−−→
AM| = |^AM
0
| =
Rt
−−→
AM = Rt e(t −
π
2
)
r
M
=
−→
OA +
−−→
AM = R e(t) +
Rt e(t −
π
2
) = {R cos t + Rt sin t; R sin t −
Rt cos t}
t
O
M
0
x
y
M
A
a b
ha, bi = ([a], b).
{O; i, j}
ha, bi = −y
a
x
b
+ x
a
y
b
=
x
a
y
a
x
b
y
b
.
1
◦
ha, bi = −hb, ai
2
◦
ε : E
2
× E
2
3 {a, b} 7→ ha, bi ∈ R
π
2
1
◦
ha, ai = 0
[6 ,6)67?,-* ** .-7-|*,0* 8-)12 M (R; 0) ‚~b-7?b*,86 -132|,-/80ƒ=
   àxÿxXWxZ ­;= 30/2,-1 Æ]= H2/8? A            0



·— 8-)16−→16/6,09 ω 0 −`−\→6 t = ∠M OA =         y
  ;**;† OA = R e(t) \ |AM | = | ^ AM | =   0


Rt \ /7*L-b68*7?,-\ AM = Rt e(t − ) =
                                               0
                    −−→
 H-~8-;2 r = −OA
                                               π
                                               2
                  → −−→
                 M   + AM = R e(t) +
            π
Rt e(t −    2)   = {R cos t + Rt sin t; R sin t −
            =                                                           A
   ðÍwÍñW W S³T͚XxXW´á â]ä \ •Ú_\ •Úã\
Rt cos t}
                                                                                 M
•Ú`\ •ò•\ •ò]\ •òÆ\ Æã]\ ÆãÚ\ Æa]\ Æa^\ ÆaÆ\                  O     t

ÆaÚ Å âÚä \ 8*;6 `=                                                         M0        x


                                                                        Ç0/= Æ]=
!    hohe mihpqeçekpe qefghihq kl mnhofhogp '
ϳTxwx™xXWxZ Š‘’ ¡ŠŒ¢”ŽªŽŒŽ’ ”Ž‰žŠŠ” a Œ b  ŠŒŽžŒŠ”Š¦
¡‹Š‰ŠžŒ ¢‘”Žž£ ‹ŽªœÀ«ŽŽ ¤Œ‹Š†
                                     ha, bi = ([a], b).
  { /0/8*;* 1--3L0,68\ -.3*L*79*;-M .36b; -38-,-3;03-b6,,; 3*.*K
3-; {O; i, j} \ 2)08b69 ‚`ƒ\ .-72)6*;
                          ha, bi = −ya xb + xa yb =
                                                          xa ya
                                                                .                    ‚Æ^ƒ
                                                          xb yb
    ™VxvTÍWñx¶yWx ¶tu̶ztÍ yu¶uVu ³TuWêtxwxXW´Z
                                     )
  1 ha, bi = −hb, ai ‚1-/-/0;;*830 ,-/8?ƒ =
    ◦

  2 ε : E × E 3 {a, b} 7→ ha, bi ∈ R · +070,*M,-* -8-+36|*,0* =
  ‡79 L-16[68*7?/8b6 ~80N /b-M/8b L-/868-),- b-/.-7?[-b68?/9 070 1--3K
    ◦
                 2    2


L0,68,-M O-3;27-M ‚Æ^ƒ 070 /b-M/8b6;0 /16793,-:- .3-0[b*L*,09 0 -.*K
36 00 .-b-3-86 ,6 2:-7 =
  —[ 1 \ b )6/8,-/80\ /7*L2*8\ )8- ha, ai = 0 =
                                π
                                2
        ◦


                                               ¸È

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