p
) A oÎ p ^p; , p ={ M ½ ^}; (*)
) A o Î l , p;
) A o, A 1, A 2Î p , .
4. 1. p, A o(x o, y o, z o), (A, B, C),
A (x x o) + B (y y o) + C (z z o) = 0. (21)
2. p, A o(x o, y o, z o),
(22)
3. p, A o(x o, y o, z o), A 1(x 1, y 1, z 1), A 2(x 2, y 2, z 2),
4. p, a, b, c
+ + = 1 (24)
(, a, b, c ).
. 1. M (x, y, z) . ^ Û = 0. (x x o, y y o, z z o), (22).
, M (x, y, z) (21), ^ Û M Îp.
2. M (x, y, z) . , , : = 0. (22).
, M (x, y, z) (22), , , , M Îp.
3. A o(x o, y o, z o), A 1(x 1, y 1, z 1), A 2(x 2, y 2, z 2), , (x 1 x o, y 1 y o, z 1 z o) (x 2 x o, y 2 y o, z 2 z o) p. (22) , (23).
4. , A (a, 0, 0), B (0, b, 0), C (0, 0, c). (23):
x a y 0 z 0
0 a b 0 0 0 = 0.
0 a 0 0 c 0
(24).
.
.
Ax + By + Cz + D = 0, (25)
. , (25) .
. , (21). D = Ax o By o Cz o= const. (25).
, p (25). A o(x o, y o, z o) . (25):
|
|
Ax o+ By o+ Cz o+ D = 0.
D = Ax o By o Cz o, (25) (21). , , .
, (25).
1. D = 0.
Ax + By + Cz = 0
O (0, 0, 0).
.
2. C = 0.
Ax + By + D = 0.
(A, B, 0) ^ Oz, , p½½ Oz.
, B = 0 p½½ Oy, A = 0 p½½ Ox.
3. A = B = 0.
Cz + D = 0,
z = C /D.
p^ Oz.
, A = C = 0
p ^ Oy, B = C = 0 p ^ Ox.