Let be an abelian category, an additive, full and self-orthogonal subcategory of closed under direct summands, the right Gorenstein subcategory of relative to , and the left orthogonal class of . For an object in , we prove that if is in the right 1-orthogonal class of , then the -projective and -projective dimensions of are identical; if the -projective dimension of is finite, then the -projective and -projective dimensions of are identical. We also prove that the supremum of the -projective dimensions of objects with finite -projective dimension and that of the -projective dimensions of objects with finite -projective dimension coincide. Then we apply these results to the category of modules.