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 Note that for any vector ar, we have
a +0
r
r
 = 0
a
a
+
=
r
r
r
Here, the zero vector 0
r  is called the additive identity for the vector addition 10 5  Multiplication of a Vector by a Scalar
Let ar  be a given vector and λ a scalar