If R divides PQ
uuur
 such that 
RQ
m
uuur  = 
nPR
uuur ,
where m and n are positive scalars, we say that the point R divides PQ
uuur  internally in the
ratio of m : n Now  from triangles ORQ and OPR, we have
RQ
uuur  = OQ
OR
b
r
−
=
−
uuur
uuur
r
r
and
PR
uuur  = OR
OP
r
a
−
=
−
uuur
uuur
r
r ,
Therefore, we have
(
)
m b
r
−
r
r  =
(
)
n r
r−a
r     (Why )
or
rr  = mb
na
m
+n
+
r
r
(on simplification)
Hence, the position vector of the point R which divides P and Q internally in the
ratio of m : n is given by
OR
uuur  = mb
na
m
+n
+
r
r
Fig 10 16
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not to be republished
VECTOR ALGEBRA
439
Case II When R divides PQ externally (Fig 10