"
"
"
 Ä„ P0 = (x0, y0, z0)
-

n = [A, B, C]
Ä„ : A(x - x0) + B(y - y0) + C(z - z0) = 0.
-

n
P =
-

(-1, 2, 0) n = [2, -3, 1]
AB A = (3, 2, -1) B = (5, 0, 7)
Ä„ : Ax + By + Cz + D = 0,
|A| + |B| + |C| > 0
D
-

n = [A, B, C] z z = - C = 0

C
P =
(3, -2, 5) xOz
Q =
(1, 3, -2) y
-

Ä„ a =
-

-

[a1, a2, a3] b = [b1, b2, b3] c = [c1, c2, c3]


x y z 1


a1 a2 a3 1

Ä„ : = 0.

b1 b2 b3 1


c1 c2 c3 1
Ä„ x, y, z
a, b, c = 0

x y z
Ä„ : + + = 1.
a b c
 Ä„ :
x + 2y + 3z - 6 = 0
l P0 = (x0, y0, z0)
-

v = [Ä…, ², Å‚]
Å„Å‚
ôÅ‚
òÅ‚x = x0 + Ä…t,
y = y0 + ²t,
ôÅ‚
ółz = z0 + łt,
-

t " R v
-

P = (-1, 0, 3) v = [2, -1, 5]
P = (1, 2, 3) Q = (3, 2, 1)
l P0 = (x0, y0, z0)
-

v = [Ä…, ², Å‚]
x - x0 y - y0 z - z0
l : = = .
Ä… ² Å‚
x - 1 y + 2 z - 5
l : = =
2 4 1
x - 1 y + 2 z x + 1 y + 11 z + 1
l1 : = = , l2 : = =
2 -1 -3 1 2 1
l
Ä„1 : A1x + B1y + C1z + D1 = 0, Ä„2 : A2x + B2y + C2z + D2 = 0,

A1x + B1y + C1z + D1 = 0,
l :
A2x + B2y + C2z + D2 = 0.

A1x + B1y + C1z + D1 = 0,
l :
A2x + B2y + C2z + D2 = 0
-

v = [A1, B1, C1] × [A2, B2, C2].

6x + 2y - z - 9 = 0,
l :
3x + 2y + 2z - 12 = 0

x + y + z + 4 = 0,
l :
3x + y - z + 2 = 0
xOz

P Ä„ P
-
-

P P Ä„"Ä„.

P l P
-
-

P P Ä„"l.
P = (3, -2, 1)
Ä„ : 2x - y + 3z = 0
P = (2, -1, 4)
x y z
l : = =
1 -1 -3
 P0 = (x0, y0, z0)
Ä„ : Ax + By + Cz + D = 0
|Ax0 + By0 + Cz0 + D|
d(P0, Ä„) = " .
A2 + B2 + C2
P = (5, -1, 6) Ä„ :
3x - 4y + 12z - 12 = 0
Ä„1 : 3x + y - z - 2 = 0 Ä„2 : 3x + y - z + 3
Å„Å‚
ôÅ‚ -2 + t,
òÅ‚x =
P = (3, 4, 2) l : y = 1 + t,
ôÅ‚
ółz = 3 - 3t,
t " R
Å„Å‚ Å„Å‚
ôÅ‚ -1 + t, ôÅ‚
òÅ‚x = òÅ‚x = s,
l1 : -1 + 2t, t " R, l2 : -1 + 2s, s " R.
y = y =
ôÅ‚ ôÅ‚
ółz = 2t, ółz = 2 - 2s,
x - 1 y + 2 z
l : = =
2 -1 1
Ä„ : 2y + 2z - 5 = 0