In view of the Observations 2 and 3, for mutually perpendicular
unit vectors 
ˆ
ˆ
,ˆ
and
i
j
k  (Fig 10 24), we have
ˆ
ˆ
i
i
×  = 
ˆ
ˆ
ˆ
ˆ
0
j
j
k
k
×
=
×
=
r
ˆ
ˆ
i
×j
= ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
,
,  
k
j
k
i
k
i
j
×
=
× =
5 In terms of vector product, the angle between two vectors   and  
a
rb
r
  may be
given as
sin θ = |
|
|
||
|
a
b
a b
×
r
r
r
r
6 It is always true that the vector product is not commutative, as a
×b
r
r
 = 
b
a
−
r×
r