whats the difference between the projection of a vector on another vector and vector along direction of another vector?

Question

thankyou

Answer 1

The projections are the same. If there is a distinction intended, they mean that the dot product of A on B is the projection of A on B times the magnitude of B whereas they mean that the dot product of A with the unit vector in the direction of B is the actual projection of A on B. In the first case the actual projection of vector A on B is (A•B)/|B| (note that this is not just the dot product) and in the second case A • (B/|B|).