CHAPTER I

Abstract

This chapter describes the real number, and vector and scalar quantities. Any physical quantity that can be completely represented by a real number is known as a scalar quantity, or simply as a scalar. Thus a scalar quantity has magnitude, including the sense of being positive, or negative, but no assigned position, and no assigned direction. A vector quantity has magnitude, and direction but no assigned position in space, as the initial point O was arbitrarily chosen. Such a vector quantity is known as a free vector. It is found that when the term vector is used, it is assumed that it refers to a free vector. It is found that if, however, the vector quantity has not only a specified magnitude, and direction, but must be located in a specified line in the given direction, the vector quantity is known as a line vector. It is found that if, on the other hand, instead of an arbitrarily-chosen origin O, there is a specified point O which must be taken as origin, then only one point A is needed to complete the representation of this restricted vector quantity which is known as a position vector, or, more precisely, as the position vector of A.