N
0
r
−a
=
ur
r
r � Equation of a plane perpendicular to a given line with direction ratios A, B, C
and passing through a given point (x1, y1, z1) is
A (x – x1) + B (y – y1) + C (z – z1 ) = 0
� Equation of a plane passing through three non collinear points (x1, y1, z1),
© NCERT
not to be republished
 MATHEMATI CS
502
(x2, y2, z2) and (x3, y3, z3) is
1
3
1
3
1
3
1
2
1
2
1
2
1
1
1
z
z
y
y
x
x
z
z
y
y
x
x
z
z
y
y
x
x
−
−
−
−
−
−
−
−
−
 = 0
� Vector equation of a plane that contains three non collinear points having
position vectors 
b
a
r,r
 and cr is  (
) [(
)
(
) ]
0
r
a
b
a
c
a
−
−
×
−
=
r
r
r
r
r
r
� Equation of a plane that cuts the coordinates axes at (a, 0, 0), (0, b, 0) and
(0, 0, c) is
=1
+
+
c
z
b
y
a
x
� Vector equation of a plane t hat passes through t he intersection of
planes
1
1
2
2
and
r n
d
r n
d
⋅
=
⋅
=
r r
r r
  is 
1
2
1
2
(
)
r
n
n
d
d
⋅
+ λ
=
+ λ
r
r
r
, where λ is any
nonzero constant � Cartesian equation of a plane that passes through the intersection of two
given planes A1 x + B1 y + C1 z + D1 = 0 and   A2 x + B2 y + C2 z + D2 = 0
is (A1 x + B1 y + C1 z + D1) + λ(A2 x + B2 y + C2 z + D2) = 0