Question

What is the projection of `<4 , -2 , 7 >` onto `< 2 , -5 , 8 >`?

Answer 1

The projection is = `74/93〈2,-5,8〉`

Explanation:

let `veca=〈2,-5,8〉` and `vecb=〈4,-2,7〉`
The dot product `=veca.vecb=8+10+56=74`
`∣veca∣^2=4+25+64=93`
The projection `=(veca.vecb)/(∣veca∣^2)veca=74/93〈2,-5,8〉`