Direction cosines
Vector of Class 11
If vector 
makes angle α, β and γ with x, y and z axes respectively, then
cosα=
where cos α, cos β and cos γ are called direction cosines of the vector. The unit vector in the direction of is
=
Illustration 10. If 
and
, find the vector having the same magnitude as 
and parallel to
.
Solution: Magnitude of =
= 5
And magnitude of = 25
Now a unit vector parallel to = 
∴ The vector having the same magnitude as and parallel to
= 25 
Illustration 11. What is the displacement of a point on a wheel initially in contact with the ground when the wheel rolls froward through half a revolution. Given radius of wheel is R.
Solution: Displacement = 
= 
tan θ = 
∴ θ = tan−1
