  We present the measurements related to the spin alignment of
$\mathrm{K^{*0}}$ and $\mathrm{\phi}$ vector mesons at mid-rapidity for Pb--Pb
collisions at $\sqrt{s_{\mathrm{NN}}}$ = 2.76 TeV using the ALICE detector at
the LHC. The second diagonal spin density matrix element ($\rho_{00}$) is
measured from the angular distribution of the decay daughters of the vector
meson in the decay rest frame, with respect to the event plane and the
production plane. The $\rho_{00}$ values are found to be less than 1/3 at low
$p_{\mathrm{T}}$ ($<$ 2 GeV/$c$) for both vector mesons. The observed
deviations from 1/3 are maximal for mid-central collisions at a level of
3$\sigma$ for $\mathrm{K^{*0}}$ and 2$\sigma$ for $\mathrm{\phi}$ mesons. As a
control measurement the \rh~values were found to be consistent with 1/3, i.e.,
no significant spin alignment, for pp collisions with respect to the production
plane. The results are qualitatively consistent with the expectation from a
model that attributes the spin alignment to a polarization of quarks in the
presence of large initial angular momentum and a subsequent hadronization by
the process of recombination.
