  We consider the cluster and backbone mass distributions between two lines of
arbitrary orientations and lengths in porous media in three dimensions, and
model the porous media by bond percolation at the percolation threshold $p_c$.
We observe that for many geometrical configurations the mass probability
distribution presents power law behavior. We determine how the characteristic
mass of the distribution scales with such geometrical parameters as the line
length, w, the minimal distance between lines, r, and the angle between the
lines, $\theta$. The fractal dimensions of both the cluster and backbone mass
are independent of w, r, and $\theta$. The slope of the power law regime of the
cluster mass is unaffected by changes in these three variables. However, the
slope of the power law regime of the backbone mass distribution is dependent
upon $\theta$. The characteristic mass of the cluster also depends upon
$\theta$, but the characteristic backbone mass is only weakly affected by
$\theta$. We propose new scaling functions that reproduce the $\theta$
dependence of the characteristic mass found in the simulations.
