Force Projection: In
some problems, we are interested in finding the projection
(component) of a force in a specified direction. Using the eye hook
example, let's see how we would find the projection of force vector
along line CD as
depicted in the figure below.
If the angle α between and line CD is known,
then the projection of force along CD is found as
If on the other hand the angle α is
not easily available, then we can use a vector operation to solve
for 
. To do this, we
must know the unit vector along CD. If there is already a vector
along that line, then we can use it to find the desired unit vector
as
Then the projection of along line CD is obtained by the dot
product
In this case, we can also find angle α as
If we did not have vector 
, then we would determine the position vector
from point C to D. The
unit vector is found by dividing by its magnitude.