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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) So
PQ =
2
2
2
(1
( 2))
(2
4)
(3
( 5))
− −
+
−
+
− −
 = 
77
Thus, the direction cosines of the line joining two points is
3
2
8
,
,
77
77
77
−
Example 4 Find the direction cosines of x, y and z-axis Solution The x-axis makes angles 0°, 90° and 90° respectively with x, y and z-axis Therefore, the direction cosines of x-axis are cos 0°, cos 90°, cos 90° i