Question

I let u = the first vector and v = the second vector. The vectors are orthornormal, except for the fact that they are not unitvectors. So I divided by the magnitude which is 3 for both vectors. So modified, i get 1/3u and 1/3v. I know that the formula forthis particular orthogonal projection is:

This would mean that:

9e1=[9 0 0 0] (in R4)

and the other dot product is -6.

However, in the book the answer is 2u - 2v. Why is my dot product off by a factor of 3?

Answer 1

You divided by 3 in the beginning, so at the end, you must divide by 3 again.

Answer 2

Actually, your answer is correct. 6u - 6v = <8,0,2,-2>, which is the answer in my textbook (Otto Bretscher, 5th edition)