Find the position vector of a point R which divides the line joining two points  P
and Q whose position vectors are 
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
2
  and –
i
j
k
i
j
k
+
−
+
+
 respectively, in the
ratio 2 : 1
(i) internally
(ii) externally
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VECTOR ALGEBRA
441
16 Find the position vector of the mid point of the vector joining the points  P(2, 3, 4)
and Q(4, 1, –2) 17 Show that the points A, B and C with position vectors, 
ˆ
ˆ
ˆ
3
4
4 ,
a
i
j
k
=
−
−
r
ˆ
ˆ
ˆ
2
b
i
j
k
=
−
+
r
 and 
ˆ
ˆ
3ˆ
5
c
i
j
k
= −
−
r
, respectively form the vertices of a right angled
triangle