(1)
Let rr be the position vector of  the point P,,
then NP
uuur
= 
dn
r
ˆ
r−
 (as ON
NP
OP
+ =
uuur
uuur
uuur
)
Therefore, (1) becomes
(
)
r
d n
d n
∧
∧
−
⋅
r
 = 0
or
(
)
r
d n
n
∧
∧
−
⋅
r
 = 0
(d ≠ 0)
or
r n
d n n
∧
∧
∧
⋅
−
⋅
r
 = 0
i e ,
r n
r⋅∧
 = d
(as
1)
∧n n
∧⋅
=
… (2)
This is the vector form of the equation of the plane Cartesian form
Equation (2) gives the vector equation of a plane, where nˆ  is the unit vector normal to
the plane