Introduction

Introduction

Many physical quantities can be sorted into two kinds. A scalar quantity is completely described by its magnitude alone -- mass, length, temperature, area, volume, time, distance, speed, work, money, voltage, density, and resistance are all scalars, and throughout this chapter every scalar is simply taken to be a real number. A vector quantity, by contrast, needs both a magnitude and a direction to describe it fully -- displacement, velocity, force, electric field, acceleration, and momentum are typical examples.

This chapter develops the algebra and geometry of vectors from the ground up: how a vector is represented and classified (section 5.1), the section formula for dividing a segment in a given ratio, the dot product of two vectors, the cross product of two vectors, and finally the triple product of three vectors.