Solution The given equation can be written as
ˆ
ˆ
ˆ
(
6
3
2
⋅
−
+
+
rr
i
j
k ) = 1 (1)
Now
ˆ
ˆ
ˆ
|
6
3
2
|
i
j
k
−
+
+
 =
36
9
4
7
+ + =
Therefore,  dividing both sides of (1) by 7, we get
6
3
2 ˆ
ˆ
ˆ
7
7
7
r
i
j
k


⋅ −
+
+




r
 = 1
7
which is the equation of the plane in the form 
r nˆ
r⋅ =d This shows that 
k
j
i
n
ˆ
27
37ˆ
67ˆ
ˆ
+
+
=−
 is a unit vector perpendicular to the
plane through the origin Hence, the direction cosines of nˆ  are 
27
,
37
,
7
−6