5) Let rr  be t he position vector of an
arbitrary point P(x, y, z), then P is a point on
the line if and only if AP
r
a
= −
uuur
r
r  and
AB
b
a
=
−
uuur
r
r  are collinear vectors Therefore,
P is on the line if and only if
(
)
r
a
b
a
−=λ −
r
r
r
r
Fig 11 5
© NCERT
not to be republished
 MATHEMATI CS
470
or
(
)
r
a
b
a
=
+ λ
−
r
r
r
r , λ ∈ R