ABSTRACT
This chapter begins with the algebra of vectors on the basis of the analytic definition of a vector. It utilizes the directed line segments or arrows to represent vectors geometrically and to give goemetric interpretations of physicists results. The study of the representation of vectors, the algebra and calculus of vectors, together with some of their various applications constitute the subject matter of vector analysis. Scalars and vectors are hardly sufficient to treat the class of quantities that are of interest in physics, engineering, and applied mathematics. The common length of the arrows represents the magnitude of the vector, and the arrowhead indicates the direction of the vector. In the analytic approach, a vector in three-dimensional space is defined as an ordered triple of real numbers relative to a given coordinate system. The axiomatic point of view treats a vector simply as an undefined entity of an abstract algebraic system called a linear vector space.
