e λb
r
 = r
a−
r
r
Conversely, for each value of the parameter λ, this equation gives the position
vector of a point P on the line Hence, the vector equation of the line is given by
rr  =
λ
r
ra +
b (1)
Remark If 
ˆ
ˆ
ˆ
b
ai
bj
ck
= + +
r
, then a, b, c are direction ratios of the line and conversely,,
if a, b, c are direction ratios of a line, then 
ˆ
ˆ
ˆ
=
+
+
br
ai
bj
ck will be the parallel to
the line