e a b
⋅
rr
= b a
⋅
r r           (Why )
Two important properties of scalar product
Property 1 (Distributivity of scalar product over addition) Let ,   and  
a b
c
rr
r  be
any three vectors, then
(
)
a
b
c
⋅
r+
r
r  =
 
 
a b
a c
⋅
+
⋅
rr
r r
Fig 10 19
© NCERT
not to be republished
VECTOR ALGEBRA
443
(i)
B
C
A
l
B
l
A
C
(ii)
A
B
C
l
(iv)
l
C
B
A
(iii)
θ
θ
θ
θ
p
p
p
p
a
a
a
a
(90 <
< 180 )
0
0
θ
(0 <
< 90 )
0
0
θ
(270 <
< 360 )
0
0
θ
(180 <
< 270 )
0
0
θ
Property 2 Let  
aand 
rb
r
 be any two vectors, and λ be any scalar