Vector Projection
Key Questions

A vector is specified by its components along the coordinate axes in a particular coordinate system.
A vector projection of a vector A along some direction is the component of the vector along that direction.
If A makes an angle#theta# with the direction in which we are to find it's projection and it's magnitude#A# , the projection is given as#A cos theta# . 
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
#theta# with the displacement. In this case the component of force along displacement does all the work.
The component of F along d is#F Cos theta# , which is nothing other than the projection of F along d.Thus, for a general case, work done is given as,
#W = F Cos theta * d# Which can be written concisely as,
#W# = F . d 
Answer:
A vector projection along any direction is the component of a given vector along that direction.
Explanation:
If we have to determine the vector projection of vector A with modulus
#A# along a direction with which the vector A makes an angle#theta# , the projection is given as,#A Cos theta# 
Answer:
Please see the explanation below
Explanation:
The vector projection of
#vecb# onto#veca# is#proj_(veca)vecb=(veca.vecb)/(veca^2)veca# Calculate the dot product
#=veca.vecb# and calculate the modulus of
#veca# #=veca#