They lie in different planes � Angle between skew lines is the angle between two intersecting lines
drawn from any point (preferably through the origin) parallel to each of the
skew lines � If  l1, m 1, n1 and l2, m 2, n2 are the direction cosines of two lines; and  θ  is the
acute angle between the two lines; then
cosθ  =  |l1l2 + m 1m 2 + n1n2|
� If a1, b1, c1 and a2, b2, c2 are the direction ratios of two lines and θ is the
acute angle between the two lines; then
cosθ = 
1
2
1
2
1
2
2
2
2
2
2
2
1
1
1
2
2
2
a a
b b
c c
a
b
c
a
b
c
+
+
+
+
+
+
� Vector equation of a line that passes through the given point whose position
vector is ar  and parallel to a given vector b
r
 is r
a
b
=
+ λ
r
r
r � Equation of a line through a point (x1, y1, z1) and having direction cosines l, m, n is
1
1
1
x
x
y
y
z
z
l
m
n
−
−
−
=
=
� The vector equation of a line which passes through two points whose position
vectors are ar  and b
r
 is 
(
)
r
a
b
a
=
+ λ
−
r
r
r
r