Properties of vector addition
Property 1 For any two vectors 
aand
rb
r
,
a
b
+
r
r
 = b
a
+
r
r
(Commutative property)
Fig 10 9
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VECTOR ALGEBRA
431
Proof Consider the parallelogram ABCD
(Fig 10 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