Question

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

Answer 1

`vec c=<5/2,-5/2,0>`

Explanation:

`vec a=<5,0,-2>`
`vec b=<1,-1,0>`
`vec a*vec b=5*1+0*(-1)+0*(-2)=5`
`"dot product between vec a and vec b;"`
`|b|=sqrt(1^2+1^2+0^2)=sqrt 2`
`vec c=(vec a*vec b)/(|b|*|b|)*vec b`
`vec c=5/(sqrt 2*sqrt 2)*<1,-1,0>`
`vec c=5/2<1,-1,0>`
`vec c=<5/2,-5/2,0>`