Quotients and direct sums

Let $U = \operatorname{span}\{(1, 0, 1)\}$ and $W = \{(x, y, z): x - y + z = 0\}$ in $\mathbb{R}^3$. (a) Show $\mathbb{R}^3 = U\oplus W$. (b) Find the projection $P$ onto $U$ along $W$. (c) Check $P^2 = P$ and $\operatorname{tr}P = 1$.