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 © NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
481
Z
Y
X
O
P(x1, y1, z1)
Example 15 Find the distance of the plane 2x –  3y + 4z – 6 = 0 from the origin Solution Since the direction ratios of the normal to the plane are 2, –3, 4; the direction
cosines of it are
2
2
2
2
2
2
2
2
2
2
3
4
,
,
2
( 3)
4
2
( 3)
4
2
( 3)
4
−
+ −
+
+ −
+
+ −
+
 , i