But
AP
r
a
=
−
uuur
r
r Therefore, (
) N
0
r
−a
⋅
=
r
r
r
       … (1)
This is the vector equation of the plane Cartesian form
Let the given point A be (x1, y1, z1), P be (x, y, z)
and direction ratios of  N
ur
 are A, B and C Then,
1
1
1 ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
,
a
x i
y j
z k
r
xi
y j
z k
=
+
+
=
+
+
r
r
 and 
ˆ
ˆ
ˆ
N
A
B
C
i
j
k
= + +
r
Now
r( – ) N= 0
a ⋅
r
r
r
So
(
)
(
)
(
)
1
1
1 ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
(A
B
C ) 0
x
x i
y
y
j
z
z
k
i
j
k


−
+
−
+
−
⋅
+
+
=


i