Question

What is the projection of `< 5 , -6, 0 >` onto `< -1, -4 , 6 >`?

Answer 1

see below

Explanation:

Use the formula `proj_a b = (a*b)/|a|^2 a`

That is,
`proj_a b =(<5,-6,0>*<-1,-4,6>)/(sqrt(5^2+(-6)^2+0^2))^2 <5,-6,0>`

`=(-5+24+0)/(25+36)<5,-6,0>`

`=19/61 <5,-6,0>`

`=<95/61, -114/61,0>`