In flat space, the classical vectors such as a position vector are bilocal (“point for head and point for tail”). The four-dimensional curved space Schwarzschild metric is mathematically similar to the metric of a sphere surface in three-dimensional flat space, where we can write an incremental displacement vector at a point on surface but cannot write position vectors along the curved surface. Similarly, in curved space, we can write an incremental displacement vector based on curved space metric, even if writing a position vector is difficult. We suggest a classical vector method based on this classical incremental vector which gives all the desired mathematical results including various identities, similar to conventional tensor analysis. We examine, if this mathematical similarity between a curved space and a sphere surface in flat space can also lead to geometrical similarity. But, we encounter some difficulties. Therefore, the curved space-time requires discarding bilocal vectors and defining vectors called the local vectors (Ref. 1). Changing definition of vectors can overcome the difficulties but we realize some new concerns. This Newtonian vector method is an easier mathematical alternative to conventional tensor analysis in the curved multidimensional space which also throws light on the geometrical concerns, if any, in describing such curved space. We can also establish relationship between the three-dimensional Lagrangian method and the four-dimensional Geodesic analysis, both giving the same results.