  We study the photo- and electro-productions of the vector kaon off the
proton, i.e., $\gamma^{(*)}p\to K^{*+}\pi^0\Sigma^0$, and investigate the line
shape of the $\pi^0\Sigma^0$ invariant mass in an effective Lagrangian approach
with the inclusion of a $K^*N\Lambda^*$ interaction. Relevant electromagnetic
form factors for the neutral hyperons and charged strange mesons are
constructed by considering experimental and theoretical information. We find
that the $\Lambda^*$ peak is clearly observed for the photo- and
electro-productions with the finite $K^*N\Lambda^*$ interaction, whereas the
clear peak signals survive only for the electro-production, when we ignore the
interaction. These different behaviors can be understood by different $Q^2$
dependences in the $K^*$ electromagnetic and $K^*\to\gamma K$ transition form
factors. We suggest a photon-polarization asymmetry $\Sigma$ to extract
information of the $K^*N\Lambda^*$ interaction. It turns out that $\Sigma$ near
the $\Lambda^*$ peak region becomes negative with a finite $K^*N\Lambda^*$
interaction while positive without it for $Q^2 = 0$, due to the different
naturalities of $K$ and $K^*$ exchanges. For $Q^2\ne 0$, we observe more
obvious signals in the peak region due to the additional contribution of the
longitudinal virtual photon for $\Lambda^*$.
