In view of the Observations 2 and 3, for mutually perpendicular unit vectors
ˆ
,ˆ ˆ
and
,
i
j
k  we have
ˆ ˆ
ˆ ˆ
i i
⋅ =j j
⋅
 = ˆ ˆ
1,
k k
⋅
=
ˆ
ˆ ˆ
ˆ
i
j
j k
⋅
=
⋅
 = ˆ ˆ
0
k i  
6 The angle between two nonzero vectors ra  and 
r
b is given by
cos
,
|
||
a b|
a b
  
r
r
r
r
 or
–1 cos
|
||
a b|
a b
⎛
⎞
θ =
⎜
⎟
⎝
⎠
rr
r
r
7 The scalar product is commutative