orthocomplement of a finite-dimensional Hilbert space

Question

Let $\mathcal{H}$ be an infinite-dimensional Hilbert space. Moreover, let $\mathcal{P}_2 \in \mathcal{H}$ and $\mathcal{P}_3 \in \mathcal{H}$ be a finite-dimensional and an infinite-dimensional closed sub-spaces of $\mathcal{H}$. In a book, the orthocomplement of $\mathcal{P}_2$ in $\mathcal{P}_2 + \mathcal{P}_3$ is indicated as: \begin{equation*} \mathcal{W} \triangleq (\mathcal{P}_2 + \mathcal{P}_3) \cap \mathcal{P}_2^\perp. \end{equation*} I cannot understated which elements are in $\mathcal{W} \in \mathcal{H}$... In may study case, I can explicitly write down $\mathcal{P}_2$, $\mathcal{P}_3$ and $\mathcal{P}_2^\perp$ but I don't know how to combine them to get $\mathcal{W}$.