1.
Ax + By + Cz + D = 0. (1)
D = 0, ,
Ax + By + Cz = 0. (2)
C = 0 (1)
Ax + By + D = 0, (3)
Oz.
B = 0 (1)
Ax + Cz + D = 0. (4)
Oy, A = 0 (1)
By + Cz + D = 0, (5)
Ox.
, - , , , . (3), (4) (5) , D = 0,
Ax + By = 0, (6)
Ax + Cz = 0, (7)
By + Cz = 0. (8)
(6) - , Oz; (7) - , Oy, (8) - , Ox. (1) A = 0 B = 0,
Cz + D = 0, (9)
xOy. B = 0 C = 0 (1)
Ax + D = 0, (10)
yOz. A = 0 C = 0 (1)
By + D = 0, (11)
(11) xOz.
, (9), (10) (11) D = 0,
z = 0, (12)
x = 0, (13)
y = 0 (14)
, xOy, yOz xOz.
2.
(15)
, - Ox, Oy Oz , , p - .
3. (1) (15)
(16)
, (1).
4.
(17)
a, b c - , .
5. , M (x 1, y 1, z 1),
A (x - x 1) + B (y - y 1) + C (z - z 1) = 0. (18)
A, B C (18) , , M (x 1, y 1, z 1).
6.
A 1 x + B 1 y + C 1 z + D 1 = 0 A 2 x + B 2 y + C 2 z + D 2 = 0 (19)
(20)
7. (19)
A 1 A 2 + B 1 B 2 + C 1 C 2 = 0. (21)
8. (19)
(22)
9. N (x 1, y 1, z 1) Ax + By + Cz + D = 0
(23)
10. :
(24)
:
(25)
t - , , , , (25), .
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11. , A (x 1, y 1, z 1), B (x 2, y 2, z 2), C (x 3, y 3, z 3)
(26)