Задачи по аналитической геометрии. Микенберг М.А. - 39 стр.

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l l a
1
x +
b
1
y + c
1
z + d
1
= 0 a
2
x + b
2
y + c
2
z + d
2
= 0
l l
α(a
1
x + b
1
y + c
1
z + d
1
) + β(a
2
x + b
2
y + c
2
z + d
2
) = 0,
α β
P P
a
1
x+b
1
y+c
1
z+d
1
= 0 a
2
x+b
2
y+c
2
z+d
2
= 0 a
3
x+b
3
y+c
3
z+d
3
= 0
P
P
α(a
1
x + b
1
y + c
1
z + d
1
) + β(a
2
x + b
2
y + c
2
z + d
2
) + γ(a
3
x + b
3
y + c
3
z + d
3
) = 0,
α β γ
ax + by + cz + d = 0
ax + by +
cz + d > 0 ax + by +
cz + d < 0
(3; 5; 1)
x + 2y + 3z 7 = 0
2x + 3y + 17z 2 = 0
(1; 4; 3) (2; 5; 0)
(2; 1; 3)