  Fundamental plane of elliptical galaxies can be used to predict the intrinsic
size of galaxies and has a number of plausible application to study cosmology
and galaxy physics. We present a detailed analysis of the fundamental plane of
the SDSS-III BOSS LOWZ and CMASS galaxies. For the standard fundamental plane,
we find a strong redshift evolution for the mean residual and show that it is
primarily driven by the redshift evolution of the surface brightness of the
galaxies. After correcting for the redshift evolution, the FP residuals are
strongly correlated with the galaxy properties and some observational
systematics. We show that the variations in the FP between the central and
satellite galaxies, that have been observed in the literature, can primarily be
explained by the correlation of the FP with the galaxy luminosity. We also
measure the cross correlations of the FP residuals with the galaxy density
field. The amplitude of the cross correlations depends on the galaxy properties
and environment with brighter and redder galaxies showing stronger correlation.
In general, galaxies in denser environments (higher galaxy bias ) show stronger
correlations. We also compare FP amplitude with the amplitudes of intrinsic
alignments of galaxy shapes (IA), finding the two to be correlated. Finally,
using the FP residuals we also study the impact of intrinsic alignments on the
constraint of growth rate using redshift space distortions. We do not observe
any significant trends in measurements of the growth rate $f$ as function of
the amplitude of FP-density correlations, resulting in null detection of the
effects of IA on the RSD measurements.
