Аналитическая геометрия. Шурыгин В.В. - 58 стр.

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dist (M
1
, `) =
|h
−−−→
M
0
M
1
, a i|
|a|
=
mod
x
1
− x
0
y
1
− y
0
x
a
y
a
p
x
2
a
+ y
2
a
.
2. ` M
0
∈ `
N {A; B} dist (M
1
, `)
−−−→
M
0
M
1
N
dist (M
1
, `) = |pr
N
(
−−−→
M
0
M
1
)| =
=
|(
−−−→
M
0
M
1
, N)|
|N|
=
|A(x
1
− x
0
) + B(y
1
− y
0
)|
√
A
2
+ B
2
.
•
•
M
0
N
`
M
dist (M
1
, `) =
|Ax
1
+ By
1
+ C|
√
A
2
+ B
2
.
E
2
dist (M
1
, `) =
|ε
ij
(x
i
1
− x
i
0
)a
j
|
p
g
ij
a
i
a
j
=
|ε
12
|mod
x
1
1
− x
1
0
x
2
1
− x
2
0
a
1
a
2
p
g
ij
a
i
a
j
dist (M
1
, `) =
|g
ij
(x
i
1
− x
i
0
)N
j
|
p
g
km
N
k
N
m
.
`
1
↑ `
2
↑ ϕ ∈
[0, π]
a
1
a
2
                                                             x1 − x0 y1 − y0
                                            mod
                                                                    ‚Úڃ
                             −−−→                               xa        ya
                          |h M0 M1 , a i|
          dist (M1 , `) =                 =                  p               .
                               |a|
     H             )                    )                       x2a + ya2
   2. 3*L.-7-|0;\ 8- .39;69 ` [6L6,6 8- 1-M M ∈ ` 0 ,-3;67?,; b*1K
8-3-; N / 1--3L0,686;0 {A; B} = „-:L6 36//8-9,0* dist (M , `) ,6N-L08/9
                                                                     0


161 6+/-7J8,69 b*70)0,6 .3-*1 00 b*18-36 −M−−M→ ,6 -/? / ,6.36b79J}0;         1


b*18-3-; N ‚/;= 30/= Æaƒ†                                    0   1



                              −−−→
        dist (M1 , `) = |prN (M0 M1 )| =
                              −−−→                                                         ‚Úòƒ
                            |(M0 M1 , N)| |A(x1 − x0 ) + B(y1 − y0 )|
                          =              =       √                    .
                                |N|                A2 + B 2
¼/70 .39;69 [6L6,6 236b,*,0*; ‚Úƃ\8- O-3K
;272 ‚Úòƒ ;-|,- .*3*.0/68?\36/13b69 /1-+K                               N
10\ b b0L*                                                                         •   M

                         |Ax1 + By1 + C|
      dist (M1 , `) =       √            .
                              A2 + B 2
                                                         Æa= `
                                                                     •



   { 6OO0,,-M /0/8*;* 1--3L0,68\ -.3*L*K           Ç0/ =
                                                                         M0


79*;-M 6OO0,,; 3*.*3-; ,6 E \ O-3;27 ‚Úڃ 0 ‚Úòƒ .30,0;6J8\ /--8K
b*8/8b*,,-\ b0L                          2



                                                             x11 − x10 x21 − x20
                                                 |ε12 |mod
     dist (M1 , `) =
                       |εij (xi1 − xi0 )aj |
                            p                =               p
                                                                 a1        a2              ‚Ú_ƒ
                               gij ai aj                       gij ai aj
0
                                         |gij (xi1 − xi0 )N j |
                          dist (M1 , `) = p                     .                          ‚Úãƒ
                                               gkm N k N m
ZÊ óVu™ µxšwS wtSµ´ ³T´µUµW ™WXW´µWZ
(:7-; ;*|L2 -30*,803-b6,,;0 .39;;0 ` ↑ 0 ` ↑ ,6[b6*8/9 2:-7 ϕ ∈
[0, π] ;*|L2 0N ,6.36b79J}0;0 b*18-36;0 a 0 a = “8-8 2:-7 ,6N-L08/9
                                                         1           2

                                                             1       2

                                 ¾Ô

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