,
 lx + my + nz = d (3)
This is the cartesian equation of the plane in the normal form �Note   Equation (3) shows that if 
ˆ
ˆ
ˆ
(
)
r
a i
b j
c k
⋅
+
+
r
= d is the vector equation
of a plane, then ax + by + cz = d is the Cartesian equation of the plane, where a, b
and c are the direction ratios of the normal to the plane Example 13 Find the vector equation of the plane which is at a distance of 
29
6
from the origin and its normal vector from the origin is 
ˆ
ˆ
ˆ
2
3
4
i
j
− +k