e , the scalar components a1, a2 and a3 of the vector ar ,
are precisely the projections of ar  along x-axis, y-axis and z-axis, respectively Further,
if ar  is a unit vector, then it may be expressed in terms of its direction cosines as
ˆ
ˆ
ˆ
cos
cos
cos
a
i
j
k
=
α +
β +
γ
r
Example 13 Find the angle between two vectors  and 
a
rb
r
 with magnitudes 1 and 2
respectively and  when  
a b1
⋅
=
rr Solution Given 
1,|
|
1and | |
2
a b
a
b
 
 
 
r
r
r
r