Question

What is the projection of `<8,-1,6 >` onto `<-1,5,-3 >`?

Answer 1

The vector projection is `〈-31/35,-31/7,93/35〉`

Explanation:

Let `vecb=〈8,-1,6〉`

and `veca=〈-1,5,-3〉`

Then the vector projection of `vecb` onto `veca` is
`=(veca.vecb)/(∣veca∣)^2*veca`
where the dot product is `veca.vecb`

dot product `(8*-1)+(-1*5)+(6*-3) =-8-5-18=-31`

and `(∣veca∣)^2=(1+25+9)=35`

so the projection is `-31/35〈-1,5,-3〉 =〈-31/35,-31/7,93/35〉`