Find the orthogonal complement $W^{\perp}$ of the subspaces $W \subset \mathbb{R}^3$ spanned by the indicated vectors. What is the dimension of $W^{\perp}$ in each case?
(a) $\left(\begin{array}{r}3 \\ -1 \\ 1\end{array}\right)$,
(b) $\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right),\left(\begin{array}{l}2 \\ 0 \\ 1\end{array}\right)$,
(c) $\left(\begin{array}{l}1 \\ 2 \\ 3\end{array}\right),\left(\begin{array}{l}2 \\ 4 \\ 6\end{array}\right)$,
(d) $\left(\begin{array}{r}0 \\ 1 \\ -1\end{array}\right),\left(\begin{array}{r}-2 \\ 3 \\ 1\end{array}\right),\left(\begin{array}{r}-1 \\ 2 \\ 0\end{array}\right)$,
(e) $\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right),\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right),\left(\begin{array}{l}0 \\ 1 \\ 1\end{array}\right)$.