Аналитическая геометрия. Шурыгин В.В. - 59 стр.

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cos ϕ =
(a
1
, a
2
)
|a
1
||a
2
|
.
`
1
`
2
a
1
a
2
ϕ
1
a
1
a
2
ϕ
2
−a
1
a
2
[0,
π
2
]
`
1
`
2
ϕ
`
1
`
2
cos ϕ =
|(a
1
, a
2
)|
|a
1
||a
2
|
.
N
1
N
2
ϕ
cos ϕ =
|(N
1
, N
2
)|
|N
1
||N
2
|
.
`
1
`
2
A
1
x+B
1
y+C
1
=
0 A
2
x + B
2
y + C
2
= 0
cos ϕ =
|A
1
A
2
+ B
1
B
2
|
p
A
2
1
+ B
2
1
p
A
2
2
+ B
2
2
.
5x −2y + 3 = 0
M(2; 3)
{5; −2}
x = 2 + 5t y = 3 − 2t
{2; 5}
2(x − 2) + 5(y − 3) = 0
∠A
ABC A(3; 1) B(−2; 4) C(1; 0)
a
.- O-3;27*
                                                  (a1 , a2 )
                                        cos ϕ =              .
   H2/8? 8*.*3? ` 0 ` · ,*-30*,803-b6,,* .39;* / ,6.36b79J}0;0
                                                  |a1 ||a2 |

b*18-36;0 a 0 a /--8b*8/8b*,,- = H2/8? ϕ · 2:-7 ;*|L2 a 0 a \ 6 ϕ ·
                          1       2


2:-7 ;*|L2 −a 0 a = ˆL0, 0[ ~80N 2:7-b .30,6L7*|08 0,8*3b672 [0, ] \ -,
              1       2                                    1               1   2       2


0 9b79*8/9 ‚.- -.3*L*7*,0Jƒ 2:7-; ;*|L2 .39;;0 ` 0 ` = (:-7 ϕ ;*|L2
                                                                                   π
                  1           2                                                    2


.39;;0 ` 0 ` ,6N-L08/9 .- O-3;27*
          1       2
                                                                   1   2



                                                  |(a1 , a2 )|
                                        cos ϕ =                .
                                                   |a1 ||a2 |
¼/70 0[b*/8, ,-3;67?,* b*18-3 N 0 N ~80N .39;N\8- 2:-7 ϕ ;-|,-
,6N-L08? 861|* .- O-3;27*                           1       2



                                                 |(N1 , N2 )|
                                       cos ϕ =                .
                                                  |N1 ||N2 |
{ /72)6*\*/70 ` 0 ` [6L6,\/--8b*8/8b*,,-\236b,*,09;0 A x+B y+C                            =
0 0 A x + B y + C = 0 \ 8-
                  1           2                                            1   1       1

     2        2           2

                                            |A1 A2 + B1 B2 |
                                  cos ϕ = p 2       p         .
                                           A1 + B12 A22 + B22
Z ˜TWµxTUZ
ðÍwÍñÍ ±Z ­-/86b08? 236b,*,0* .*3.*,L0127936 1 .39;-M 5x − 2y + 3 = 0 \
.3-N-L9}*:- )*3*[ 8-)12 M (2; 3) =
   àxÿxXWxZ €6.36b79J}0; b*18-3-; 0/1-;-:- .*3.*,L0127936 9b79*8/9
b*18-3 / 1--3L0,686;0 {5; −2} = H-~8-;2 .*3.*,L012793 0;**8 /7*L2J}0*
.636;*830)*/10* 236b,*,09† x = 2 + 5t Å y = 3 − 2t =
   ‡32:-M b6306,8 36//2|L*,0M† ,-3;67?,; b*18-3-; 0/1-;-:- .*3.*,K
L0127936 9b79*8/9 b*18-3 / 1--3L0,686;0 {2; 5} \ .-~8-;2 .*3.*,L012793
0;**8 236b,*,0* 2(x − 2) + 5(y − 3) = 0 =
   ðÍwÍñÍ ±Z ­-/86b08? 236b,*,0* +0//*1830/ 2:76 ∠A 83*2:-7?,016
ABC / b*3I0,6;0 A(3; 1) \ B(−2; 4) 0 C(1; 0) =
   àxÿxXWxZ —[ 0[b*/8,-:- /b-M/8b6 L06:-,67*M 3-;+6 /7*L2*8\ )8- L79
8-:-\ )8-+ .-72)08? b*18-3\ L*79}0M .-.-76; 2:-7 ;*|L2 b*18-36;0 a
                                    ¾Ù

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