Post on 07-Jan-2016
description
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---
1
9
OAOBAB =
:
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. :
)()()(|)()(| ABOAOBABOA + :
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---
1
11
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(i) 00 ======== 0 ==== (ii) )()()( ======== (iii) ==== )( (iv) ==== )( (v) ==== 0 , ==== (vi) ==== 0 , ==== .
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---
AB
B ()
A ()
1
13
AB .
OM :
AMOAOM +=
BMOBOM += .
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OBOABMOBAMOAOM +=+++=2 .
2OBOAOM +=
xx ,
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Ox .
iOI
==== x x . Ox Ox , Ox Ox .
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iOM
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14
xx y y
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Oxy . y y , xx 1M , xx , y y 2M . x 1M xx y 2M y y , x y . .
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y y xx , . .
x y M x y( , ) ( , )x y .
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3: jyix ++++==== .
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j
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y
y
x
1
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.: . -.
---
AB
B ()
A ()
1
15
: Oxy .
OA = . 1A 2A xx y y , :
21 OAOAOA += (1)
yx, A ,
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j . , jyix += . jyixjyix +=+ jyyixx )()( = xx , 0 xx ,
i y yx x
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j . xx = , yy = . :
jyix ++++==== .
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yj
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16
, x
y
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+ = + + + = + + +( ) ( ) ( ) ( )x i y j x i y j x x i y y j1 1 2 2 1 2 1 2 jyixjyix )()()( 1111 +=+=
+ = + +( , )x x y y1 2 1 2
= ( , )x y1 1
),(),(),( 21212211 yyxxyxyx ++=+
),(),( 1111 yxyx =
,
+ :
),(),(),( 21212211 yyxxyxyx ++=+=+
.
),( 11 yx ),( 22 yx ),( yx .
.
.
.: . -.
---
1
17
)(
21 OBOAOM +=
),( yxOM = , ),( 11 yxOA= , ),( 22 yxOB=
: )],(),[(21),( 2211 yxyxyx +=
++=
2,
22121 yyxx
221 xxx
+=
221 yyy
+= .
),( 11 yx ),( 22 yx ),( yx
AB .
:
OAOBAB = , ),( yxAB= , ),( 22 yxOB=
),( 11 yxOA= : ),(),(),(),( 12121122 yyxxyxyxyx == . :
),( yx ),( 11 yxA ),( 22 yx
12 xxx = 12 yyy = .
:
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MA 1
18
),( yx=
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21
21
21
22 ||||)()()()()(|| yxyx +=+=+=+== :
),( yx= , 22|| yx +=
, )12,5(= , 13125|| 22 =+= .
( , )x y1 1 ),( 22 yx . )(
),( 1212 yyxxAB = ,
22|| yx += :
212
212 )()()( yyxx +=
:
( , )x y1 1 ),( 22 yx
212
212 )()()( yyxx += .
.
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a
A1
y
x
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y
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---
1
19
= ( , )x y A
aOA = . , Ox ,
x x . : 20
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= ( , )3 1
= ( , )3 3 -,
det( , )
=
=
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20
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.
:
1 1
2 2
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=
x yx y
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2
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:
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= ( , )x y1 1
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1 1 1 21 2 2 1 1 2
2 2 1 2
// 0x y y y
x y x yx y x x
= = = =
.
,
1 2 :
1 2// =
.
.: . -.
22 : x yx y
1 1
2 2= 1 2 1 2x y y x
det( , )a =
x yx y
1 1
2 2
---
1
21
),( 11 yx=
),( 22 yx=
.
0
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= . ,
),(),( 2211 yxyx = : 21 xx = 21 yy = ,
x y y x x y y x1 2 1 2 2 2 2 2 0 = =
022
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MA 1
22
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= 0
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i j
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;
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A
F
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---
1
23
= ( , )x y1 1
= ( , )x y2 2 .
OA =
OB
= .
+= ))((2)()()( 222 ,
,,
. :
( ) ( ) ( ) 2 2 1 2 2 1 2= + x x y y , ( ) 2 12 12= +x y ( ) 2 22 22= +x y . , :
+++=+ ))((2)()( 22222121212212 yxyxyyxx
+++=+++ ))((222 22222121212221212221 yxyxyyyyxxxx
= ))(( , :
1 2 1 2x x y y = +
,
= ( , )x y1 1 ,
= ( , )x y2 2
= ( , )x y3 3 , : (1) 1 1 2 2 1 2 1 2 1 2 1 2( ) ( , )( , ) ( ) ( ) ( )x y x y x x y y x x y y = = + = + =
( ) =
1 1 2 2 1 2 1 2 1 2 1 2( ) ( , )( , ) ( ) ( ) ( )x y x y x x y y x x y y = = + = + =
( ) =
: ( ) ( ) ( )
= =
1 2 1 2 = + = + = + = +
x x y y
:
(1) ( ) ( ), R = = = = = = = =
(2) ( ) + = + + = + + = + + = +
(3) 1 2 1 = = = =
a
y
x
(x1,y1)
(x2,y2)
.: . -.
= ( , )1 2
= ( , )31 , :
2 2 2 2
1 3 2 1
1 2 3 1
+ = =
+ +
5 1 225 10 2
= = =
=4
.
-
.
MA 1
24
(2) + = + + = + + +( ) ( , )( , ) ( ) ( )x y x x y y x x x y y y1 1 2 3 2 3 1 2 3 1 2 3
= + + + = + + +( ) ( ) ( ) ( )x x x x y y y y x x y y x x y y1 2 1 3 1 2 1 3 1 2 1 2 1 3 1 3= +
(3) 1 2 1 2 1 2 1 20 0x x y y y y x x = + = =
1 21 2
1 2
1 1y yx x
= =
= ( , )x y1 1
= ( , )x y2 2 ,
=| | | | , ||||
==== .
,
= +x x y y1 2 1 2 , | | = +x y12 12 | |
= +x y22
22
.
: 22
22
21
21
2121yxyx
yyxx
++++++++
++++====
v
, 0
.
OA =
OM = .
OA 1M .
1OM
. :
=1OM
.
:
==+=+= OMMMOMMMOMv 11111 )(
: =
.
.
a
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