  The relation space of a hyperplane arrangement is the vector space of all
linear dependencies among the defining forms of the hyperplanes in the
arrangement. In this paper, we study the relationship between the relation
space and the Orlik--Terao ideal of an arrangement. In particular, we
characterize spanning sets of the relation space in terms of the Orlik--Terao
ideal. This result generalizes a characterization of 2-formal arrangements due
to Schenck and Toh\v{a}neanu \cite[Theorem 2.3]{ST}. We also study the minimal
prime ideals of subideals of the Orlik--Terao ideal associated to subsets of
the relation space. Finally, we give examples to show that for a 2-formal
arrangement, the codimension of the Orlik--Terao ideal is not necessarily equal
to that of its subideal generated by the quadratic elements.
