Exercise 5.  Show that the nonzero vectors   and   are perpendicular iff  .

Solution 5.

See text and/or instructor's solution manual.

Let    and  .  

Since neither nor equals zero, they are perpendicular iff their dot product is zero: .   

Their dot product is

          

This solution is complements of the authors.

(c) 2008 John H. Mathews, Russell W. Howell