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 
:
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 
onto Excercise 2-7.
Find the component of vector 
along the direction of vector 
. After finding this component, find the orthogonal projection of 
onto 
. 
along the direction of vector . After finding this component, find the orthogonal projection of onto . 
can be found by applying the definition of vector components:
that lies along the direction of 
. In order to find the orthogonal projection we simply need to multiply the unit vector 
by 5: