  (Abridged) We have observed velocity resolved spectra of four ro-vibrational
far-infrared transitions of C3 between the vibrational ground state and the
low-energy nu2 bending mode at frequencies between 1654--1897 GHz using HIFI on
board Herschel, in DR21(OH), a high mass star forming region. Several
transitions of CCH and c-C3H2 have also been observed with HIFI and the IRAM
30m telescope. A gas and grain warm-up model was used to identify the primary
C3 forming reactions in DR21(OH). We have detected C3 in absorption in four
far-infrared transitions, P(4), P(10), Q(2) and Q(4). The continuum sources MM1
and MM2 in DR21(OH) though spatially unresolved, are sufficiently separated in
velocity to be identified in the C3 spectra. All C3 transitions are detected
from the embedded source MM2 and the surrounding envelope, whereas only Q(4) &
P(4) are detected toward the hot core MM1. The abundance of C3 in the envelope
and MM2 is \sim6x10^{-10} and \sim3x10^{-9} respectively. For CCH and c-C3H2 we
only detect emission from the envelope and MM1. The observed CCH, C3, and
c-C3H2 abundances are most consistent with a chemical model with
n(H2)\sim5x10^{6} cm^-3 post-warm-up dust temperature, T_max =30 K and a time
of \sim0.7-3 Myr. Post warm-up gas phase chemistry of CH4 released from the
grain at t\sim 0.2 Myr and lasting for 1 Myr can explain the observed C3
abundance in the envelope of DR21(OH) and no mechanism involving
photodestruction of PAH molecules is required. The chemistry in the envelope is
similar to the warm carbon chain chemistry (WCCC) found in lukewarm corinos.
The observed lower C3 abundance in MM1 as compared to MM2 and the envelope
could be indicative of destruction of C3 in the more evolved MM1. The timescale
for the chemistry derived for the envelope is consistent with the dynamical
timescale of 2 Myr derived for DR21(OH) in other studies.
