Question

What is the projection of `<-7 , 3, -5 >` onto `< 4, 0, -2 >`?

Answer 1

The projection is `=-9/10〈4,0,-2〉`

Explanation:

Let `vecb=〈-7,3,-5〉` and `veca=〈4,0,-2〉`
The projection of `vecb` onto `veca`

`=(veca.vecb)/(∥veca∥*∥veca∥)veca`

The dot product is `=veca.vecb=〈-7,3,-5〉.〈4,0,-2〉=-28+0+10=-18`

The modulus of `veca=∥veca∥=∥〈4,0,-2〉∥=sqrt(16+4)=sqrt20`

Therefore the projection is `=-18/20〈4,0,-2〉=-9/10〈4,0,-2〉`