  Let $\mathcal{F}_1$ and $\mathcal{F}_2$ be transverse two dimensional
foliations with Gromov hyperbolic leaves in a closed 3-manifold $M$ whose
fundamental group is not solvable, and let $\mathcal{G}$ be the one dimensional
foliation obtained by intersection. We show that $\mathcal{G}$ is
\emph{leafwise quasigeodesic} in $\mathcal{F}_1$ and $\mathcal{F}_2$ if and
only if the foliation $\mathcal{G}_L$ induced by $\mathcal{G}$ in the universal
cover $L$ of any leaf of $\mathcal{F}_1$ or $\mathcal{F}_2$ has Hausdorff leaf
space. We end up with a discussion on the hypothesis of Gromov hyperbolicity of
the leaves.
