ABSTRACT
This chapter resolves vectors and tensors along a triad of base vectors that are right-handed and orthonormal, that is, mutually orthogonal and of unit length. Thus, given a set of base vectors, there is a one-to-one correspondence between vectors and ordered triples of numbers. Analytic geometry is the numerical representation of geometric objects. The basic idea is the establishment of a one-to-one correspondence between ordered triples of numbers and points or locations in three-dimensional space. Any tensor can be expressed in terms of components along an orthonormal basis. The components of a tensor are completely determined by its action on the base vectors. The Cartesian components of the identity and permutation tensors are the Kro-necker delta and permutation symbol, respectively. In practical applications vectors and tensors are usually represented by numerical components. For instance, the vector quantity force requires three numbers for its specification. Tensor equations are usually solved in a particular coordinate system.
