Question

What is the projection of `<0,8,5>` onto `<1,2,-4>`?

Answer 1

`-4/sqrt(21)`

Explanation:

The projection of a vector `A` along a direction `theta` with itself is given as `|A|costheta`

Lets say here `A = <0,8,5>`
And `B = <1,2,-4>`

Their dot product is `|A| |B| costheta = 0+16-20 =-4`

So the projection is `(|A||B|costheta)/(|B|) = (-4)/sqrt(1^2+2^2+4^2) = -4/sqrt(21)`