© 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 e , 
2
3
4
,
,
29
29
29
−
Hence, dividing the equation 2x – 3y + 4z – 6 = 0 i