10) Let AB
and BC
,
a
b
 
 
uuur
uuur
r
r
 then using
the triangle law, from triangle ABC, we have
AC
uuur  =
a+
rb
r
Now, since the opposite sides of a
parallelogram are equal and parallel, from
Fig 10 10, we have, AD = BC = b
uuur
uuur
r
 and
DC = AB = a
uuur
uuur
r Again using triangle law, from
triangle ADC, we have
AC
uuuur  = AD + DC =
b+
a
uuur
uuur
r
r
Hence
a
b
+
r
r
 = b
a
+
r
r
Property 2 For any three vectors ,
a band
c
rr
r
(
)
a
b
c
+
+
r
r
r  =
(
)
a
b
c
+
+
r
r
r
(Associative property)
Proof Let the vectors ,
a band
c
rr
r be represented by PQ,  QR  and  RS
uuur
uuur
uuur , respectively,
as shown in Fig 10