11(i) and (ii) Fig 10 11
Then
a
b
+
r
r
 = PQ + QR = PR
uuur
uuur
uuur
and
b
c
+
r
r  = QR + RS = QS
uuur
uuur
uuur
So
(
)
 
a
b
c
+
r+
r
r  = PR + RS = PS
uuur
uuur
uur
Fig 10 10
© NCERT
not to be republished
 MATHEMATICS
432
a
a
1
2
1
2
a
–2
a
a
2
and
(
)
a
b
c
+
+
r
r
r  = PQ + QS = PS
uuur
uuur
uur
Hence
(
)
a
b
c
+
+
r
r
r  =
(
)
a
b
c
+
+
r
r
r
Remark The associative property of vector addition enables us to write the sum of
three vectors 
,
,
  as 
a
b
c
a
b
c
+
+
r
r
r
r
r
r  without using brackets