  Using the notion of inclination of two subspaces $L$ and $M$ of Hilbert space
$\mathcal{H}$, we prove the theorem on the extension of linear continuous
functionals defined on the subspace $L$ to $\mathcal{H}$ so that the extended
functionals vanish on the subspace $M$. We apply this theorem to study the
question of decomposition of the electromagnetic field in resonator with
ideally conducting walls into potential and vortex components and derive the
Korn-type inequality for vortex fields.
