what is the definition partial vapor pressure
The vapor pressure is the partial pressure at equilibrium of a substance in the gas phase when the conditions (T,P) are such that the substance should normally be in the liquid phase (as per the phase diagram). Therefore, the second sentence.
Vapor pressure or equilibrium vapor pressure is defined as the pressure exerted by a vapor in thermodynamic equilibrium with its condensed phases (solid or liquid) at a given temperature in a closed system. The equilibrium vapor pressure is an indication of a liquid's evaporation rate.