  We show that affine subspaces of Euclidean space are of Khintchine type for
divergence under certain multiplicative Diophantine conditions on the
parametrizing matrix. This provides evidence towards the conjecture that all
affine subspaces of Euclidean space are of Khintchine type for divergence, or
that Khintchine's theorem still holds when restricted to the subspace. This
result is proved as a special case of a more general Hausdorff measure result
from which the Hausdorff dimension of W(\tau) intersected with an appropriate
subspace is also obtained.
