, . , .
:
-
- + + z + D = 0, (9.1)
= (, , ) , ( );
-
, (9.2)
, (, 0, 0), (0, , 0), (0, 0, ) - ;
- , ( 0, 0, z 0) = (, , )
( - 0) + ( - 0) + (z - z 0) = 0, (9.3)
-
cos a + cos b + z cos g - p = 0, (9.4)
- , a, b, g - , ;
- , ( 1, 1, z 1), ( 2, 2, z 2),
( 3, 3, z 3)
(9.5)
(9.1) (9.4) :
m D <0.
d ( 0, 0, z 0) (9.1) :
d = (9.6)
1 + 1 + 1 z + D 1 = 0
2 + 2 + 2 z + D 2 = 0 :
(9.7)
:
1/ 2 = 1/ 2 = 1/ 2, (9.8)
:
1 2 + 1 2 + 1 2 = 0. (9.9)
.
) 2 + 4 - 5 z + 21 = 0 .
, D >0,
) , (1, 2, 3) (3, 2, 1).
(9.3) 3( - 1) + 2( - 2) + (z - 3) = 0
3 + 2 + z - 10 = 0.
) , (3, 2, -1) 3 - 5 + 2 z - 10 = 0.
, .. (3, -5, 2) . (9.3)
3( - 3) - 5( - 2) + 2(z + 1) = =0 3 - 5 + 2 z + 3 = 0.
) , (2, -1, 4) (3, 2, -1) + + 2 z - 3 = 0.
. , , . , + + 2 z - 3 = 0, .. = (1, 1, 2). , = ´ 1.
|
|
,
= = (11, -7, -2).
(9.3) 11( - 2) - 7( + 1) - 2(z - 4) = 0
11 - 7 - 2 z -21 = 0.
)
, (9.5):
..
: (9.7):
.
:
. (9.10)
(9.11)
( 1, 1, z 1) - , , = (l, m, n) - , , - .
, ( 1, 1, z 1) ( 2, 2, z 2), :
(9.12)
. ,
(9.12),
,
:
:
(9.13)
:
l 1/ l 2 = m 1/ m 2 = n 1/ n 2. (9.14)
:
l 1 l 2 + m 1 m 2 + n 1 n 2 = 0. (9.15)
.
) .
z:
,
)
( -2)/2 = (- 1)/3 = (z - 3)/1.
.
, . = (2, 3, 1) , = 2 + 3 + z = 0. :
, (9.12), :
x = y /(-2) = z/ 4.
) ( + 1)/2 = ( - 1)/(-1) = (z - 2)/3 , / (- 1) = ( + 2)/2 = (z - 3)/(-3).
..
1 = (2, -1, 3) 2 = (-1, 2, -3) ( ) , 1 2 , .. .
,
3(-1, 1, 1).
( + 1)/2 = ( - 1)/(-1) = (z - 2)/3 . , (-1, 1, 2), , . ,
-( + 1) + ( - 1) + (z -2) = 0 - - z + 4 =0.
10.