  Recently, Ghosh \& Haynes \cite{HG} proved a Khintchine-type result for the
problem of Diophantine approximation in certain projective spaces. In this note
we complement their result by observing that a Jarn\'{\i}k-type result also
holds for `badly approximable' points in real projective space. In particular,
we prove that the natural analogue in projective space of the classical set of
badly approximable numbers has full Hausdorff dimension when intersected with
certain compact subsets of real projective space. Furthermore, we also
establish an analogue of Khintchine's theorem for convergence relating to
`intrinsic' approximation of points in these compact sets.
