From the possible solutions below which is correct if: a= <4,1,3> and b= <-2,2,1>, then proj [sub]b a =?

Question

possible solutions....



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>

or is it none of these?

Answer 1

proj_b a = (a.b) b / ||b||^2
Now a.b = 4(-2) + 1(2) + 3(1) = 0. So proj_b a = <0, 0, 0>.