  We find, from our study of binary spiral galaxies in the Sloan Digital Sky
Survey Data Release 6, that the relative orientation of disks in binary spiral
galaxies is consistent with their being drawn from a random distribution of
orientations. For 747 isolated pairs of luminous disk galaxies, the
distribution of phi, the angle between the major axes of the galaxy images, is
consistent with a uniform distribution on the interval [0 degrees, 90 degrees].
With the assumption that the disk galaxies are oblate spheroids, we can compute
cos(beta), where beta is the angle between the rotation axes of the disks. In
the case that one galaxy in the binary is face-on or edge-on, the tilt
ambiguity is resolved, and cos(beta) can be computed unambiguously. For 94
isolated pairs with at least one face-on member, and for 171 isolated pairs
with at least one edge-on member, the distribution of cos(beta) is
statistically consistent with the distribution of cos(i) for isolated disk
galaxies. This result is consistent with random orientations of the disks
within pairs.
