Pointing

In this work we treat the following problem. Given two vectors of same length, find an orthogonal transformation that transforms one to the other. This problem arises in different engineering categories. In particular, this problem arises in aerospace engineering where it is called pointing problem. In this paper we establish the theoretical background of the pointing problem in n and thus also in 3-D. We give a straightforward solution to this problem, but since it is not unique we widen the scope of the problem, define the notions of minimal pointing and optimal pointing, and require that the sought matrix be, not only orthogonal, but also a minimal, or an optimal, pointing. We then give an illustrative solution in 3-D and then extend the solution to n-D using two different approaches which we present and prove. Several examples are given in 3-D and 4-D. The 3-D examples are used to illustrate the characteristics of the solution