Then l = cos 900 = 0, m = cos 600 = 1
2,
n = cos 300 = 2
3 Example 2 If a line has direction ratios 2, – 1, – 2, determine its direction cosines Solution Direction cosines are
2
2
2
)2
(
)1
(
2
2
+−
+−
,  
2
2
2
(2)
)1
(
2
1
+−
−
+
−
,  
(
)
2
2
2
)2
(
1
2
2
+−
−
+
−
or
 2
1
2
,
,
3
3
3
−
−
Example 3 Find the direction cosines of the line passing through  the two points
(– 2, 4, – 5) and (1, 2, 3) © NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
467
Solution We know the direction cosines of the line passing through  two points
P(x1, y1, z1) and Q(x2, y2, z2) are given by
2
1
2
1
2
1
,
,
PQ
PQ
PQ
x
x
y
y
z
z
−
−
−
where
PQ =
(
)
12
2
12
2
2
1
2
)
(
)
(
z
z
y
y
x
x
−
+
−
+
−
Here P is (– 2, 4, – 5) and Q is (1, 2, 3)