Answer:
w = (-5, 5)T v = (5, 1)T kv = (-3.8, -.8)T u = (-1.3, 5.6)T
w = (-5, 5)T v = (5, 1)T kv = (-3.8, -.8)T u = (-1.3, 5.6)T
Those answers were done by reading off the picture. No guarantee that they are accurate. So let us check:
First: Does w = kv + u?
(-3.8, -0.8)T + (-1.3, 5.6)T = (-5.1, 4.8)T = w (almost)
Next: Does v · u = 0.0 ?
(5, 1)T · (-1.3, 5.6)T = -6.5 + 5.6= -0.9 = 0.0 (not quite)
Can the projection of w onto v point in the opposite direction of v ?