Find the angle formed when [4,4,2] and [4,3,12] are placed tail-to-tail; then find the components of the vector that results when [4, 3, 12] is projected onto [4, 4, 2].

Answer 1

can someone plz help me

Answer 2

use the dot product.
[4,4,2] dot [4,3,12] = |[4,4,2]| |[4,3,12]| cosØ
16 + 12 + 24 = √36 √169 cosØ
52 = (6)(13) cosØ
cosØ = 2/3
Ø = appr 48.19° or .841 radians

let u be the projection vector of [4,3,12] onto [4,4,2):
cosØ = |u|/|[4,3,12]|
|u| = 13coØ = 13(2/3) = 26/3

a unit vector along [ 4,4,2] = (1/6)[4,4,2]

so vector u = (26/3)(1/6)[4,4,2]
= (13/9)[4,4,2,] or [52/9 , 52/9 , 26/9]
=

Answer 3

wait...why is it 13cos(theta)? Where did the 13 come from?
Also, why do I have to use a unit vector? Could you please explain each step because I am a little confused some of the steps?

Answer 4

Man, reiny explained it pertty well