Аналитическая геометрия. Шурыгин В.В. - 60 стр.

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b a b
a
|a|
+
b
|b|
|b|a + |a|b
∠A
r = r
A
+ (|
−→
AC|
−→
AB + |
−→
AB|
−→
AC) t .
M(2; 1) `
2x
1
− 3x
2
− 5 = 0
g
11
= 4 g
12
= 8 g
22
= 25
ω e
1
e
2
cos ω =
(e
1
, e
2
)
|e
1
||e
2
|
=
g
12
√
g
11
√
g
22
=
4
5
=⇒ sin ω =
3
5
.
|ε
12
| = |he
1
, e
2
i| = |e
1
||e
2
|sin ω = 6
M
0
(1; −1) ∈ `
−−−→
M
0
M
{1; 2}
` a{3; 2}
dist (M, `) =
6 · mod
1 2
3 2
√
4 · 9 + 2 · 8 · 6 + 25 · 4
=
12
√
58
.
N{N
1
; N
2
} ` g
ij
a
i
N
j
= 0 ⇐⇒ 4 · 3 ·
N
1
+ 8 · 3 · N
2
+ 8 · 2 · N
1
+ 25 · 2 · N
2
= 0
AA
0
BB
0
CC
0
ABC
(r − r
A
,
−−→
BC) = 0, (r − r
B
,
−→
CA) = 0 (r − r
C
,
−→
AB) = 0.
(48)
0 = 0
0 b \ L-/868-),- b[98? /2;;2 b*18-3-b\ 1-770,*63,N b*18-36; a 0 b 0
0;*J}0N -L0,61-b2J L70,2\ ,6.30;*3\ + 070 |b|a + |a|b = „610;            a     b
-+36[-;\ +0//*1830/6 2:76 ∠A 0;**8 /7*L2J}** 236b,*,0*†                 |a|   |b|


                                             −→ −→ −→ −→
                                  r = rA + (|AC|AB + |AB|AC) t .
   ðÍwÍñÍ ±Z €6M80 36//8-9,0* -8 8-)10 M (2; 1) L- .39;-M ` \ [6L6,,-M
236b,*,0*; 2x − 3x − 5 = 0 b ,*1-8-3-M 6OO0,,-M /0/8*;* 1--3L0,68\
                    1             2
*/70 0[b*/8, g = 4 \ g = 8 \ g = 25 =
   àxÿxXWxZ H2/8? ω · 2:-7 ;*|L2 e 0 e = „-:L6
                        11            12               22

                                                                    1   2
                                 (e1 , e2 )    g12      4                                              3
            cos ω =                         =√ √      =                       =⇒             sin ω =     .
                                 |e1 ||e2 |   g11 g22   5                                              5
ˆ8/JL6  .-72)6*; |ε | = |he , e i| = |e ||e | sin ω = 6 =
  ‡67**\ M (1; −1) ∈ ` \ b*18-3 −M−−M
                                 12
                                    → 0;**8 1--3L0,68
                                           1       2
                                                          {1; 2} \ ,6.36b79K
                                                                    1   2


J}0; b*18-3-; .39;-M ` 9b79*8/9 b*18-3 a{3; 2} \ -812L6 .- O-3;27* ‚Ú_ƒ
            0                                               0


,6N-L0;
                                                                        1 2
                                                       6 · mod
                                                                        3 2 12
                    dist (M, `) = √                                       =√ .
   >8-+ b-/.-7?[-b68?/9 O-3;27-M ‚Úãƒ\ /,6)676 ,2|,- ,6M80 ,-3;67?K
                                               4 · 9 + 2 · 8 · 6 + 25 · 4    58

,M b*18-3 N{N ; N } .39;-M ` 0[ 236b,*,09 g a N = 0 ⇐⇒ 4 · 3 ·
                             1    2
                                                                                    ij
                                                                                         i       j

N + 8 · 3 · N + 8 · 2 · N + 25 · 2 · N = 0 =
  1             2                     1                         2
   ðÍwÍñÍ ÊZ ‡-16[68?\ )8- b/-8 83*2:-7?,016 .*3*/*16J8/9 b -L,-M
8-)1* ‚.30,6L7*|68 -L,-;2 .2)12 .39;Nƒ=
   àxÿxXWxZ {/-8 AA \ BB 0 CC 83*2:-7?,016 ABC 0;*J8\ /--8b*8K
                                      0        0                0
/8b*,,-\ 236b,*,09
      (r − r , BC) = 0, (r − r , CA) = 0 0 (r − r , AB) = 0.               ‚Úaƒ
               −−→                  −→                        −→
­0/8*;6 83*N 236b,*,0M (48) /-b;*/8,6\ .-/1-7?12\ 161 7*:1- .3-b*308?\
            A                                      B                                         C



0N /2;;6 */8? 8-|L*/8b- 0 = 0 =
   àxyuµxXwSxµÍ´ ™WzxTÍzSTÍá âãä \ 7*1 09 •òÅ â•ä \ :76b6 @\ åòÅ âòä \ :76b6 ò\
åå•\ ]=
   ðÍwÍñW W S³T͚XxXW´á â]ä \ ]•^\ ]••\ ]•]\ ]•Æ\ ]•Ú\ ]•ã\ ]]Ú\ ]òa\ ]_Æ\ ]_Ú\
]_ò\ ]__\ ]_ã\ ]_`\ ]ãò\ ]aÆ\ ]`•\ ]`Æ\ Æ^^\ Æ^•Å âÚä \ 8*;6 •Ú =
                                       ÁÝ

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