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 e A (x – x1) + B (y – y1) + C (z – z1) = 0
Example 17 Find the vector and cartesian equations of the plane which passes through
the point (5, 2, – 4) and perpendicular to the line with direction ratios 2, 3, – 1 Fig 11