� If l, m, n are the direction cosines of a line, then l2 + m 2 + n2 = 1 � Direction cosines of a line joining two points P(x1, y1, z1) and Q(x2, y2, z2) are
2
1
2
1
2
1
,
,
PQ
PQ
PQ
x
x
y
y
z
z
−
−
−
where PQ =   
(
)
12
2
2
1
2
2
1
2
)
(
)
(
z
z
y
y
x
x
−
+
−
+
−
� Direction ratios of a line are the numbers which are proportional to the
direction cosines of a line � If l, m, n are the direction cosines and a, b, c are the direction ratios of a line
© NCERT
not to be republished
 MATHEMATI CS
500
then
l = 
2
2
2
c
b
a
a
+
+
; m = 
2
2
2
c
b
a
b
+
+
; n = 
2
2
2
c
b
a
c
+
+
� Skew lines are lines in space which are neither parallel nor intersecting They lie in different planes