Home  18.013A  Chapter 3  Section 3.3 


Express the component of v perpendicular to w in terms of dot products.
Solution:
The component of v perpendicular to w is the magnitude of the
projection of v perpendicular to w. By definition
this projection is v minus the projection of v in the direction
of w.
But the projection of v in the direction of w is
The projection of v normal to w is then ,
the component of v normal to w is then the square root of the
dot product of this projection with itself, or
