Remark If α, β and γ are the direction angles of vector 
1
2
3 ˆ
ˆ
ˆ
a
a i
a j
a k
=
+
+
r
, then its
direction cosines may be given as
3
1
2
ˆ
cos
, cos
,  and  cos
ˆ
|
|
|
|
|
|
|
|| |
a
a
a
a i
a
a
a
a i
 
  
 
  
  
r
r
r
r
r
Also, note that |
a| cos ,  | |cos  and | |cos
a
a
α
β
γ
r
r
r
 are respectively the projections of
ar  along OX, OY and OZ i 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