Аналитическая геометрия. Часть I. Шурыгин В.В. - 24 стр.

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•
•
A
O
x
2
x
1
x
3
•
•
•
A
B
O
r
A
r
B
v =
−→
AB
−→
AB = v
r
B
= r
A
+
−→
AB,
−→
AB = r
B
− r
A
, x
i
B
= x
i
A
+ v
i
, v
i
= x
i
B
− x
i
A
.
i
r
A
= x
i
A
e
i
= x
1
A
e
1
+ x
2
A
e
2
i i = 1
A B C
(
) B 6= C
(ABC) = (AB, C) =
−→
AC
−−→
CB
.
(ABC) C
( ) AB
A B C
AB (ABC) = λ λ(r
B
− r
C
) = (r
C
− r
A
)
r
C
=
r
A
+ λr
B
1 + λ
=⇒ x
i
C
=
x
i
A
+ λx
i
B
1 + λ
, i = 1, 2, 3. (3)
            x3                                                           −→
                                                                     v = AB                       B
                                                                                              •
                                                            A•
                           A
                           •                                                             rB
                 •                                             rA
                     O                   x2

 x1
                                                                             •
                                                                                 O

            Ç0/= •]=                                Ç0/= •Æ=
   H2/8? −AB
           →
              = v \ 8-:L6 0;*J8 ;*/8- /7*L2J}0* O-3;27\ /b9[b6J}0*
1--3L0,68 8-)*1 0 b*18-3-b†
              −→ −→
   r = r + AB, AB = r − r , x = x + v , v = x − x . i      i     i   ‚•]ƒi           i    i

   ð͵xñÍXWxZ {/* bI*216[6,,* O-3;27 /.36b*L70b 0 ,6 .7-/1-/80\
      B     A                        B    A         B      A                         B    A


8-7?1- b /72)6* .7-/1-/80 0,L*1/ i .30,0;6*8 Lb6 [,6)*,09\ 6 ,* 830†
r = x e = x e + x e = “80 |* O-3;27 /.36b*L70b 0 L79 .39;-M\
36//;6830b6*;-M 161 /6;-/8-98*7?,M :*-;*830)*/10M -+*18 36[;*3,-K
          i          1         2
 A        A i        A 1       A 2


/80 •\ .30 ~8-; 0,L*1/ i +2L*8 .30,0;68? b/*:- -L,- [,6)*,0* i = 1 =
ÊZ± ˜Tu¶zux uzXuÿxXWx zTxõ zuñxy ³T´µuÌ Z
ϳTxwx™xXWxZ ›Šž‘’ ŠžŠÄŽŒŽ’ žŽÐ žŠ¤Ž‰ A ¥ B Œ C ¥ ¡Œª‹Žº
»«ŒÐ ¡£’Š¦ ( ¡£’£ ’Š»Žž ¬‘žŸ ¡Š‹Š»Ž ” ¡Šžž”Ž¥ 
¡‹Š‰ŠžŒ Œ‹Œª ’žŒ”žŸ£ ’ ¡Š Ž¬Ž) Œ ž‰ŒÐ¥ ¤žŠ B 6= C ¥ º
¢‘”Žž£ ‹Ž œÀ«ŽŽ ¤Œ‹ŠÛ
                                                                     ‚•Æƒ
                                             −→
                                             AC
                         (ABC) = (AB, C) = −−→ .
ߞŠ ¤Œ‹Š (ABC) ¢‘”Àž ž‰»Ž ŠžŠÄŽŒŽ’    CB
                                                  ¥  ” ‰ŠžŠŠ’ žŠ¤‰ C
ªŽ‹Œž ( ¡”‹Ž‘¦) ŠžŽ¢Š‰ AB =
   H2/8? 8-)10 A 0 B L6, 0 83*+2*8/9 ,6M80 8-)12 C \ L*79}2J -83*[-1
                                —          )
AB b -8,-I*,00 (ABC) = λ = [ ‚]ƒ .-72 6*; λ(r − r ) = (r − r ) \
-812L6                                                               B           C            C       A


                     rA + λrB                         xiA + λxiB
                rC =                 =⇒       xiC   =            ,   i = 1, 2, 3.                     (3)
                       1+λ                               1+λ
                                               ï¸

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