  We investigate off-limb active region and quiet Sun corona using
spectroscopic data. Active region is clearly visible in several spectral lines
formed in the temperature range of 1.1--2.8 MK. We derive electron number
density using line ratio method, and non-thermal velocity in the off-limb
region up to the distance of 140 Mm. We compare density scale heights derived
from several spectral line pairs with expected scale heights as per hydrostatic
equilibrium model. Using several isolated and unblended spectral line profiles,
we estimate non-thermal velocities in active region and quiet Sun. Non-thermal
velocities obtained from warm lines in active region first show increase and
later show either decrease or almost constant value with height in the far
off-limb region, whereas hot lines show consistent decrease. However, in the
quiet Sun region, non-thermal velocities obtained from various spectral lines
show either gradual decrease or remain almost constant with height. Using these
obtained parameters, we further calculate Alfv\'en wave energy flux in the both
active and quiet Sun regions. We find significant decrease in wave energy
fluxes with height, and hence provide evidence of Alfv\'en wave damping.
Furthermore, we derive damping lengths of Alfv\'en waves in the both regions
and find them to be in the range of 25-170 Mm. Different damping lengths
obtained at different temperatures may be explained as either possible
temperature dependent damping or measurements obtained in different coronal
structures formed at different temperatures along the line-of-sight.
Temperature dependent damping may suggest some role of thermal conduction in
the damping of Alfv\'en waves in the lower corona.
