TABLE OF CONTENTS Many of the design equations contained in earlier chapters require that the user be familiar with vector algebra. It is the intent of this appendix to provide, for those who are unfamiliar with this subject, a working knowledge of vector addition, subtraction, multiplication, and division.
As illustrated in Fig. B-1, a vector may be expressed in either rectangular or polar form. In rectangular form, the vector quantity is expressed as a sum of its coordinate parts. Thus, the vector A shown in Fig. B-1 can be expressed as the sum of 5 units in the x direction and 5 units in the y direction, or A = 5 + j5. That same vector may be expressed in polar notation as a distance ( R) from the point of origin at an angle ( ?) from the x axis. If vector A were measured, its length would be found to be 7.07 units at an angle of 45 from the x axis. Thus,
Similarly, vector B can be expressed in rectangular form as 5 ? j10 or in polar form as 11.18 ? ?63.4 . Note that negative angles are measured clockwise from the x axis while positive angles are measured counterclockwise.
Rather than plotting a vector to graphically determine its component parts, it is more convenient to perform a few simple mathematical calculations.
