Аналитическая геометрия. Шурыгин В.В. - 55 стр.

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λ µ
x
1
+2x
2
+5 = 0 2x
1
−3x
2
−2 = 0
8x
1
+ 2x
2
+ 7 = 0
`
λ(x
1
+ 2x
2
+ 5) + µ(2x
1
− 3x
2
− 2) = 0 ⇐⇒
(λ + 2µ)x
1
+ (2λ − 3µ)x
2
+ (5λ − 2µ) = 0.
` 8x
1
+ 2x
2
+ 7 = 0
λ+2µ
8
=
2λ−3µ
2
λ = 2 µ = 1 λ µ
λ : µ 4x
1
+ x
2
+ 8 = 0
AB BC CA
ABC C
0
A
0
B
0
(BCA
0
) = λ
1
(CAB
0
) = λ
2
(ABC
0
) = λ
3
AA
0
BB
0
CC
0
λ
1
λ
2
λ
3
= 1
A B C
0
C
B
0
A
0
B
0
B
C
0 C
A
0
A
{O; e
i
}
O = A e
1
=
−→
AB e
2
=
−→
AC
236b,*,0*; ‚Æaƒ .30 ,*1-8-3N λ 0 µ = {/J /-b-12.,-/8? .39;N ‚Æaƒ .30
~8-; 861|* ,6[b6J8 .2)1-; ‚,*/-+/8b*,,;ƒ .39;N =
   ­7*L2J}0* .30;*3 .-16[b6J8\ 161 .2)10 ;-:28 ~OO*180b,- .30;*K
,98?/9 .30 3*I*,00 :*-;*830)*/10N [6L6)=
   ðÍwÍñÍ ±Z ­-/86b08? 236b,*,0* .39;-M\ .3-N-L9}*M )*3*[ 8-)12 .*3*K
/*)*,09 .39;N x +2x +5 = 0 0 2x −3x −2 = 0 0 .63677*7?,-M .39;-M
                            1           2                1       2

8x + 2x + 7 = 0 =
  1       2
   àxÿxXWxZ (36b,*,0* 0/1-;-M .39;-M ` ;-|,- [6.0/68? b b0L*†
                      λ(x1 + 2x2 + 5) + µ(2x1 − 3x2 − 2) = 0 ⇐⇒

                           (λ + 2µ)x1 + (2λ − 3µ)x2 + (5λ − 2µ) = 0.
„61 161 ` .63677*7?,6 .39;-M 8x + 2x )+ 7 = 0 \ 8- = \ -812L6
                                                     1       2                 λ+2µ        2λ−3µ

λ = 2 \ µ = 1 ‚λ 0 µ /2}*/8b*,, / 8- ,-/8?J L- .3-.-3 0-,67?,-/80
                                                                                 8           2


λ : µ ƒ 0\ /7*L-b68*7?,-\ 0/1-;69 .39;69 0;**8 236b,*,0* 4x + x + 8 = 0 =              1       2
    ðÍwÍñÍ ± Z ‚„*-3*;6 >*bƒ €6 /8-3-,6N AB \ BC 0 CA 83*2:-7?,016
                )                      )
ABC L6, 8- 10 C \ A 0 B 8610*\ 8- (BCA ) = λ \ (CAB ) = λ 0
                ‡          )
(ABC ) = λ = -16[68?\ 8- .39;* AA \ BB 0 CC .30,6L7*|68 -L,-K
                                0           0    0                        0        1           0        2


;2 .2)12 ‚8- */8?\ .*3*/*16J8/9 b -L,-M 8-)1* 070 .63677*7?,ƒ 8-:L6 0
      0           3                                          0        0        0


8-7?1- 8-:L6\ 1-:L6 λ λ λ = 1 =     1 2 3



                                B0
                  C                                                       C0                           C

                                                                                   A
                                                                                                   A0
                      A0

 A                         B                    C0               B0                        B

                           Ç0/= Æò=
  àxÿxXWxZ ­;= 30/2,-1 Æò= Ç6//;-830; 6OO0,,M 3*.*3 {O; e } \ :L*
                         −→ { ~8-; 3*.*3* b*3I0, 83*2:-7?,016 0
O = A \ e = AB \ e = AC =
                                                                                                   i
              −→
36//;6830b6*;* ,6 *:- /8-3-,6N 8-)10 0;*J8 /7*L2J}0* 1--3L0,68†
              1                     2



                                 ¾¾

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