Finding the Projection of a Vector onto a Subspace

[Dustinsfl]

Let S be a subspace of R³ spanned by u₂=$$\left[ \begin{array} {c} \frac{2}{3} \\ \frac{2}{3} \\ \frac{1}{3} \end{array} \right]$$ and u₃=$$\left[ \begin{array} {c} \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}} \\ 0 \end{array} \right]$$.
Let x=$$\left[ \begin{array} {c} 1 \\ 2 \\ 2 \end{array} \right]$$. Find the projection of p of x onto S.

I know how to find projection but I am not sure about doing the projection on a subspace.

 

[lanedance]

how about finding an orthogonal basis of S (orthonormal is even better), then the projection of x onto each basis vector...?

 

[lanedance]

or equivalently, S represents a plane in $\mathbb{R}^3$, so find the projection of X on that plane...