What are vector projections used for?
Vector projections are used for determining the component of a vector along a direction.
Let us take an example of work done by a force F in displacing a body through a displacement d.
It definitely makes a difference, if F is along d or perpendicular to d (in the latter case, the work done by F is zero).
So, let us for now assume that the force makes an angle
The component of F along d is
Thus, for a general case, work done is given as,
Which can be written concisely as,