The orthogonal projection of a vector onto another vector is a vector that has a magnitude equal to and direction equal to the direction of . Another way to think of an orthogonal projection is that it is the vector that would represent the "shadow" that casts onto if a light were held directly above and at a degree angle to .

We already know how to find the magnitude of this vector by finding so we simply need to rescale by this magnitude. Thus, we normalize and multiply by :
Figure 2-10.
Orthogonal Projection of onto
Excercise 2-7.
  Find the component of vector along the direction of vector . After finding this component, find the orthogonal projection of onto .