  We demonstrate the existence of `planar', or `type-II', radiation zeros in
5-parton QCD scattering processes. That is, the Born amplitudes are shown to
completely vanish for particular kinematic configurations, when all the
particle 3-momenta lie in a plane. This result is shown to follow particularly
simply from the known BCJ relations between the colour-ordered tree amplitudes,
and the MHV formalism is used to express the additional kinematic constraint as
a relatively simple expression in terms of only rapidity differences between
the final-state partons. In addition, we find that zeros exist for non-planar
configurations of the final-state partons, but for which the normal `type-I'
conditions on the particle four-momenta do not generally apply. We present
numerical results and comment on the possibility of observing planar radiation
zeros in hadronic collisions, via central exclusive three-jet production.
