TABLE OF CONTENTS In a rectangular system of coordinates, a vector can be completely specified by its components. These components depend, of course, upon the orientation of the coordinate system, and the same vector may be described by many different triplets of components, each of which refers to a particular system of axes. The three components that represent a vector in one set of axes, will be related to the components along another set of axes, as are the coordinates of a point in the two systems. In fact, the components of a vector may be regarded as the coordinates of the end of the vector drawn from the origin. This fact is expressed by saying that the scalar components of a vector transform as do the coordinates of a point. It is possible to concentrate attention entirely on the three components of a vector and to ignore its geometrical aspect. A vector would then be defined as a set of three numbers that transform as do the coordinates of a point when the system of axes is rotated. It is often convenient to designate the coordinate axes by numbers instead of letters x, y, z so that the components of a vector will be a 1, a 2, and a 3. The designation for the whole vector is a i, where it is understood that the subscript i can take on the value 1, 2, or 3. A...
