Question

What is the projection of `< -3 , 1 ,3 >` onto `< 8 , 8 , -4 >`?

Answer 1

The answer is `(-14/9,-14/9,7/9)`

Explanation:

The vectorprojection of `vecu` onto `vecv` is
`=(vecu.vecv.) /(vecv*vecv)*vecv`
here `vecu=(-3,1,3)` and `vecv=(8,8,-4)`
Applying this we get
`=(-24+8-12)/(64+64+16)*vecv=-28/144*vecv=-7/36*vecv`
so the answer is `((-7*8)/36,(-7*8)/36,(4*7)/36)=(-14/9,-14/9,7/9)`
or `7/9*(-2,-2,1)`