  The transverse-momentum ($p_{\rm T}$) spectra of ${\rm K}^*(892)^0$ and
$\phi(1020)$ measured with the ALICE detector up to $p_{\rm T}$ = 16 GeV/$c$ in
the rapidity range $-1.2 < y < 0.3$, in p-Pb collisions at the center-of-mass
energy per nucleon-nucleon collision $\sqrt{s_{\rm NN}}$ = 5.02 TeV are
presented as a function of charged particle multiplicity and rapidity. The
measured $p_{\rm T}$ distributions show a dependence on both multiplicity and
rapidity at low $p_{\rm T}$ whereas no significant dependence is observed at
high $p_{\rm T}$. A rapidity dependence is observed in the $p_{\rm
T}$-integrated yield (d$N$/d$y$), whereas the mean transverse momentum ($\left<
p_{\rm T} \right>$) shows a flat behavior as a function of rapidity. The
rapidity asymmetry ($Y_{\rm asym}$) at low $p_{\rm T}$ ( < 5 GeV/$c$) is more
significant for higher multiplicity classes. At high $p_{\rm T}$, no
significant rapidity asymmetry is observed in any of the multiplicity classes.
Both ${\rm K}^*(892)^0$ and $\phi(1020)$ show similar $Y_{\rm asym}$. The
nuclear modification factor ($Q_{\rm CP}$) as a function of $p_{\rm T}$ shows a
Cronin-like enhancement at intermediate $p_{\rm T}$, which is more prominent at
higher rapidities (Pb-going direction) and in higher multiplicity classes. At
high $p_{\rm T}$ (> 5 GeV/$c$), the $Q_{\rm CP}$ values are greater than unity
and no significant rapidity dependence is observed.
