Projections

The good way to understand projections is to see a couple of diagrams. Thus, given two vectors a^→ and b^→ we want to find out the projection of b^→ onto a^→. The projection is represented by Proj_a→ b^→.

 Here are a couple of diagrams illustrating the projection.

Thus, to get the projection of b^→ onto a we drop straight down from the end of b till we hit and form a right angle along with the line which is parallel to a . after that the projection is the vector that is parallel to a , starts at similar point both of the original vectors started at and ends where the dashed line hits the line parallel to a .

There is a formula for finding the projection of b^→ onto a^→.  The formula is as follow:,

Proj_a→ b^→ = a^→• b^→ / (||a^→||²) (a^→)