Question

What is the projection of `<-4,8,9 >` onto `<8,1,-1 >`?

Answer 1

The projection is `=<-4,-1/2, 1/2>`

Explanation:

The vector projection of `vecv` onto `vecu` is

`proj_uv= (vec u. vecv ) /(||vecu||)^2*vecu`

Here,

`vecv= < -4,8,9>` and

`vecu = <8,1,-1>`

The dot product is

`vecu.vecv =<-4,8,9> . <8,1,-1>`

`=(-4*8)+(8*1)+(9*-1) =-32+8-9=-33`

The magnitude of `vecu` is

`=||<8,1,-1 >|| = sqrt((8)^2+(1)^2+(-1)^2)`

`=sqrt(64+1+1)=sqrt66`

The vector projection is

`proj_uv=-33/66* <8,1,-1> = <-4,-1/2, 1/2>`