Answer:
[tex]Proj_{v}U=\frac{u\cdot v}{\left\lVert v \right\rVert^2}v=\frac{-1-5+4}{\left(\sqrt{(-1)^2+(1)^2+(1)^2}\right)^2}(-1,1,1)=\left(\frac{2}{3},-\frac{2}{3},-\frac{2}{3}\right).[/tex]
Step-by-step explanation:
The orthogonal projection of U along V is a vector defined by [tex]Proj_{v}u=\lambda v[/tex] such that [tex]v\cdot(u-\lambda v)=0.[/tex]. From here we obtain that [tex]\lambda=\frac{u\cdot v}{\left\lVert v \right\rVert ^{2}}.[/tex]
