  [Abridged] We apply the multipole vector framework to full-sky maps derived
from the first year WMAP data. We significantly extend our earlier work showing
that the two lowest cosmologically interesting multipoles, l=2 and 3, are not
statistically isotropic. These results are compared to the findings obtained
using related methods. In particular, the planes of the quadrupole and the
octopole are unexpectedly aligned. Moreover, the combined quadrupole plus
octopole is surprisingly aligned with the geometry and direction of motion of
the solar system: the plane they define is perpendicular to the ecliptic plane
and to the plane defined by the dipole direction, and the ecliptic plane
carefully separates stronger from weaker extrema, running within a couple of
degrees of the null-contour between a maximum and a minimum over more than
120deg of the sky. Even given the alignment of the quadrupole and octopole with
each other, we find that their alignment with the ecliptic is unlikely at >98%
C.L., and argue that it is in fact unlikely at >99.9% C.L. We explore the role
of foregrounds showing that the known Galactic foregrounds are unlikely to lead
to these correlations. Multipole vectors, like individual a_lm, are very
sensitive to sky cuts, and we demonstrate that analyses using cut skies induce
relatively large errors, thus weakening the observed correlations but
preserving their consistency with the full-sky results. Finally we apply our
tests to COBE cut-sky maps and briefly extend the analysis to higher
multipoles. If the correlations we observe are indeed a signal of non-cosmic
origin, then the lack of low-l power will very likely be exacerbated, with
important consequences for our understanding of cosmology on large scales.
