The interaction forces between a nanosphere and a flat plate in undersaturated vapors are examined. We perform grand canonical Monte Carlo simulations, where the surfaces of the sphere and the plate are treated as rigid smooth and the vapors are modeled as a Lennard-Jones fluid of nonpolar spherical molecules. The following results are obtained: (i) The force between the sphere and plate becomes attractive at the surface distances where capillary condensation takes place in the gap between the surfaces; (ii) the onset of the attractive force becomes farther as the relative vapor pressure increases; (iii) the curve of the pull-off force (or the adhesion force) as a function of the relative vapor pressure has a peak, where the peak position shifts to a higher relative pressure and the peak height becomes smaller with decreasing the attractive interaction of the surfaces with a fluid molecule; (iv) at the relative vapor pressure where the pull-off force becomes maximum, the coverage of the surface by fluid molecules is about 0.45 regardless of the strength of the surface-fluid attraction; in addition, the gap between the sphere and plate exhibits the same feature of wetting, that is, a circular string of fluid molecules plus an adsorbed layer on each surface. The results of our simulations will be compared in details with those of force measurements by the atomic force microscope and the surface force apparatus.