I'm not sure how to compute this problem.... If a = <4, 1, 3> and b = <-2, 2, 1>, then proj [sub]b a = ?

Question

If a = <4, 1, 3> and b = <-2, 2, 1>, then proj [sub]b a =

these are the possible answers to choose from....

a. (-1)<-2, 2, 1>
b. (-1/3)<-2, 2, 1>
c. (-2/9)<-2, 2, 1>
d. (-1/9)<-2, 2, 1>
e. <0, 0, 0>
f. (2/9)<-2, 2, 1)
g. (1/3)<-2, 2, 1>
h. <-2, 2, 1>
i. none of these

Answer 1

proj_b a = ((a . b) / ||b||) b
a.b = -8 + 2 + 3 = -3, ||b|| = √(4+4+1) = 3
So proj_b a = (-3 / 3) b = (-1) b, so answer (a) is correct.