Abstract
This chapter explains real numbers, scalar quantities, and vector 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 or direction. Examples of scalars are mass, energy, time, work, power, electrical resistance, and temperature. If there is a space Σ in which a point O has been arbitrarily chosen as an origin, then any point A in Σ may be said to define both a magnitude, represented by the distance between O and A, and a direction, represented by the direction from O to A. Any quantity that can be completely represented by such a pair of points O and A is known as a vector quantity or a vector. When the term vector is used, it is assumed that it refers to a free vector.
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