. . . .
, , , , , .
.
, 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 , .
.
.
(α1 α2) :
A1x+B1y+C1z+D1 =0 A2x+B2y+C2z+D2 =0,
, , n 1={ A1,B1,C1) n 2={ A2,B2,C2). (5.6) , α1 α2
|
|
(8.4)
:
(8.5)
:
A1A2 + B1B2 + C1C2 = 0. (8.6)
. 1(1, 1, z1), M 2(x2, y2, z2) M 3(x3, y3, z3), . 1 2 ={ x2 - x1, y2 - y1, z2 - z1 }, 1 3 ={ x3 - x1, y3 - y1, z3 - z1 } 1 ={ x - x1, y - y1, z - z1 }, (x, y, z) , . , . , :
(8.7)
, , , z , , , .
, 7, :
(8.8)
, , cosα, cosβ, cosγ . :
, (8.9)
x0,y0,z0 . (8.9) , , , . D.
, 7.
.
. . .
,
A1x+B1y+C1z+D1= 0 A2x+B2y+C2z+D2 =0, A1,B1,C1 A2,B2,C2 :
A1x+B1y+C1z+D1 =0 (8.10)
A2x+B2y+C2z+D2 =0.
, .
, 0(x0,y0,z0) a ={l,m,n}.
8.1. , , .
(x,y,z), , 0 = { x - x0,y - y0,z - z0) . :
(8.11)
.
, , :
1(1, 1, z1) M2(x2, y2, z2), 1 2 = { x2 x1, y2 - y1, z2 - z1 }, (8.11) :
- (8.12)
- , .
(8.11) t, :
|
|
. (8.13)
, (8.10) , , . , , . [ n1n2 ] . , , , (8.10), , .
.
.
[ n1n2 ]. n 1 = {2,1,-3}, n 2 = {1,-5,4}. [ n1n 2 ] = {-11,-11,-11}. , {1,1,1}.
z0=0. 0 0 , 0=2, 0=1. :
.
:
.
. - 0, , 0.