4
© NCERT
not to be republished
THREE D IMENSIONAL G EOMETRY
469
These are parametric equations of the line Eliminating the parameter λ from (2),
we get
1
x – x
a
 =
1
1
y – y
=z – z
b
c (3)
This is the Cartesian equation of the line �Note   If l, m, n are the direction cosines of the line, the equation of the line is
1
x – x
l
 =
1
1
y – y
=z – z
m
n
Example 6 Find the vector and the Cartesian equations of the line through the point
(5, 2, – 4) and which is parallel to the vector 
ˆ
ˆ
ˆ
3
2
8
i
j
k
+
−