Solution Comparing the given equation with the standard form
1
1
1
x
x
y
y
z
z
a
b
c
−
−
−
=
=
We observe that
x1 = – 3, y1 = 5, z1 = – 6; a = 2, b = 4, c = 2 © NCERT
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THREE D IMENSIONAL G EOMETRY
471
Thus, the required line passes through the point (– 3, 5, – 6) and is parallel to the
vector 
ˆ
ˆ
ˆ
2
4
2
i
j
k
+
+ Let rr  be the position vector of any point on the line, then the
vector equation of the line is given by
ˆ
ˆ
ˆ
(
3
5
6 )
r
i
j
r=− + −k
+ λ 
ˆ
ˆ
ˆ
(2
4
2 )
i
j
k
+
+
11 4  Angle between Two Lines
Let L1 and L2 be two lines passing through the origin
and with direction ratios a1, b1, c1 and a2, b2, c2,
respectively