  We use principal angles between two subspaces to define Jordan planes. Jordan
planes provide an optimal way to decompose $\mathbb{C}^n$ in relation to given
two subspaces. We apply Jordan planes to show that two pairs of of subspaces
$(M,N)$ and $(M^{\perp},N^{\perp})$ are unitarily equivalent if $M$ and $N$ are
subspaces of $\mathbb{C}^n$ in generic position. We compute numerical ranges of
sum and product of two orthogonal projections by using Jordan planes.
