Question

Find the projection of u = 4,8 onto v = 3, 12.

Answer 1

proj of u onto v is dot product of u and v divided by magnitude of v:
dot(u,v) = (4,8)(3,12) = 4*3 + 8*12 = 12 + 96 = 108
magnitude of v = sqrt(3^2 + 12^2) = sqrt(9 + 144) = sqrt(153)

so Proj of u onto v = 108/sqrt(153) in the direction of v

Answer 2

Ahhh i remember this but you left out the next parts :P

Answer 3

proj v u = (u * v/ |v|^2) v

So then after what you got, i distribute v, being 3, 12, and i get some random number, then you input w1 (what we just got, and subtract u, and ofcourse you need the same denominator, so you multiply the numbers by sqrt(153), then thats w2, and then the answer is w1+w2=u