  The variational theorem for the scattering length in the presence of the
dipole-dipole interaction is developed. The theorem is applied to the spinless
dipolar Bose gas in three dimensions. We calculated analytically the long-range
tails of the single-particle momentum distribution and static structure factor,
and the pair distribution function at short distances. The momentum
distribution is inversely proportional to $q^4$ with the anisotropic prefactor.
In the absence of the dipole-dipole interaction, Tan's adiabatic sweep theorem
is reproduced as a particular case. For the homogeneous dilute Bose gas, all
the relations are calculated analytically.
