Question

What is the projection of (4,4) onto (-7,3)?

A) -0.28(4,4)
B) -0.50(-7,3)
C) -0.28(-7,3)
D) 0.50(4,4)

Answer 1

Let's define the vectors:
u = (4,4)
v = (- 7.3)
The projection of u on v is:
P = ((u.v) / (v ^ 2)) v
We have then:
u.v = (4,4). (- 7.3)
u.v = (4) * (- 7) + (4) * (3) = -28 + 12 = -16
v ^ 2 = (- 7) ^ 2 + (3) ^ 2 = 49 + 9 = 58
Substituting we have:
P = ((- 16) / (58)) (- 7, 3)
Rewriting:
P = -0.28 (-7, 3)
Answer:
the projection of (4,4) onto (-7,3) is:
C) -0.28 (-7.3)