  We study the three-body radiative decays $B\to \phi(\rho) K\gamma$ induced by
a flavor-changing neutral current in the perturbative QCD approach.
Pseudoscalar-vector ($PV$) distribution amplitudes (DAs) are introduced for the
final-state $\phi K$ ($\rho K$) pair to capture important infrared dynamics in
the region with a small $PV$-pair invariant mass. The dependence of these $PV$
DAs on the parton momentum fraction is parametrized in terms of the Gegenbauer
polynomials, and the dependence on the meson momentum fraction is derived
through their normalizations to time-like $PV$ form factors. In addition to the
dominant electromagnetic penguin, the subleading chromomagnetic penguin,
quark-loop and annihilation diagrams are also calculated. After determining the
$PV$ DAs from relevant branching-ratio data, the direct $CP$ asymmetries and
decay spectra in the $PV$-pair invariant mass are predicted for each $B\to
\phi(\rho) K\gamma$ mode.
