Find the scalar and vector projections of b onto a.

Question

a = <3, −4> b = < 6, 0>

compab
projab

Answer 1

by definition,
the scalar projection of b onto a
is b•a/|a|
= (18+0)/5 = 18/5

If I recall the vector projection of b on a is simply the unit vector a/|a| times the scalar projection of b onto a

so a/|a| = [3/5, -4/5]
so finally the vector projection would be
(18/5)[3/5 , -4/5]
= [54/25 , -72/25] which is a vector