  A two component nonlocal vector nonlinear Schr\"odinger equation (VNLSE) is
considered with a self-induced $ {\cal PT}$ symmetric potential. It is shown
that the system possess a Lax pair and an infinite number of conserved
quantities and hence integrable. Some of the conserved quantities like number
operator, Hamiltonian etc. are found to be real-valued, in spite of these
charges being non-hermitian. The soliton solution for the same equation is
obtained through the method of inverse scattering transformation and the
condition of reduction from nonlocal to local case is also mentioned. An
inhomogeneous version of this VNLSE with space -time modulated nonlinear
interaction term is also considered and a mapping of this Eq. with standard
VNLSE through similarity transformation is used to generate its solutions.
