w = (4, 8.2)T v = (2.8, 1.75)T kv = (5.8, 1.6)T u = (-1.8, 6.4)T
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)
Think about all possible vectors w and v and the projection of w onto v.