(6) Consider the vectors Vector a=(1,2,3) and Vector b=(-3,0,2).

Question

(a) Determine the projection of Vector a onto Vector b.
(b) A unit vector is a vector of length 1. Determine a simplified unit vector in the same direction as Vector a .

Answer 1

projection of a onto b = a dot b /|b|
= ( (1,2,3) dot (-3,0,2) )/√(9+0+4)
= (-3 + 0 + 6)/√13 = 3/√13

unit vector a = (1/√(1+4+9)(1,2,3)
= (1/√14 , 2/√14 , 3/√14)