.. .
.
0 (x0,y0) n = {A,B }. , (,) , n.
( 0) + ( 0) = 0 - (7.3)
, .
. n .
(7.3) :
+ + (-0 0) = 0.
-0 0 = , :
+ + = 0. (7.4)
, 0 (x0,y0) q = {l,m }. , (,) , q,
, (7.5)
. q . , 1(1,1) 2(2,2), , (7.5) :
- (7.6)
.
l, , k , ,
l :
= kx + b - (7.8)
. . . .
, , , , , .
.
, 0(0 ,0 ,z0) n = { A,B,C }, . (, , z) 0 = { x - x0 , y - y0, z - z0) n, , :
A(x - x0) + B(y - y0) + C(z - z0) = 0. (8.1)
, , .
(8.1) :
Ax + By + Cz + D = 0, (8.2)
D = -Ax0 - By0 - Cz0. .
.
, , , D , (8.2) .
:
1) D = 0 Ax + By + Cz = 0 .
2) = 0 n = {0, B,C } Ox, , By + Cz + D = 0 .
3) = 0 Ax + Cz +D = 0 .
4) = 0 Ax + By + D = 0 z.
|
|
5) = = 0 Cz + D = 0 ( ).
6) = = 0 + D = 0 z.
7) B = C = 0 Ax + D = 0 z.
8) = D = 0 By + Cz = 0 .
9) B = D = 0 + z = 0 .
10) C = D = 0 - Ax + By = 0 Oz.
11) A = B = D = 0 z = 0 .
12) A = C = D = 0 = 0 z.
13) B = C = D = 0 = 0 z.
( ), : (8.3) . 7. , b , .
, , , :
, : .
-- .
(7)- (7) , .. a, b, c : - , b - , - Oz.
- :
- , ; - .
- , .
:
1) ,.. :
A1 x + B1 y + C1 z + D1 = 0, A2 x + B2 y + C2 z + D2 = 0;
2) M1(x1, y1, z1) M2(x2, y2, z2), , , :
=
3) M1(x1, y1, z1), , a (m, n, ), . :
:
: y= kx + b
:
:
:
:
23.
:
. , , .
1: , .
:
, 1 2 - , , 1 2
. , , .. . 1 2, 1 2, ,
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. , (1 2), . . .
: , , , .
2: , , .
:
- , , - , , - , . , . , . . , .. . . . , . ...
(4.22) , , , :
, , .
. , , , , , .. (.4.20,), :
24.
, .
1.
, .
2.
, (, ). .
3.
, , . .
25.
. , . , - . . - . . , , .
, . . , , , . .
, , .
, , :
. .
, , , . .
. . . : . -- : . . : , .
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. .
. , , , -- . . .
26.
.
. -- , , ,
n , 0 , n , . 11.9. , , . . , . , , : . , .
27,28,29. :
:
: