A good answer might be:

  w   =   (4, 8.2)T       v   =   (2.8, 1.75)T
kv   =   (5.8, 1.6)T       u   =   (-1.8, 6.4)T

Check the Answer

The above answers look good to me (especially since I drew the picture), but let us see if they are reasonable.

First: Does w  =  kv + u?

(5.8, 1.6)T + (-1.8, 6.4)T  =  (4, 8.0)T  =  w   (well, almost)

Next: Does v · u  =  0.0 ?

(5.8, 1.6)T · (-1.8, 6.4)T  =  -10.44 + 10.24  =  -0.2 =  0.0   (nearly)


QUESTION 11:

Think about all possible vectors w and v and the projection of w onto v.

  1. Is it possible for the vector kv to be longer than v?
  2. Is it possible for the vector kv to be longer than w?