Chapter 3 Vectors
Many quantities in physics require both direction and magnitude for their description. For instance, when a force acts on a body, the response of the body depends not only the strength of the force but also the direction of the force. Similarly, to describe the displacement of a body, you need to record both how far and which way.
Quantities that have both direction and magnitude are called vectors. They are represented by arrows that point in the direction of the action and whose lengths give the magnitude in appropriate units. Their addition, subtraction, multiplication and division follow separate set of rules than ordinary numbers. In this chapter we will study algebra of vectors, whose understanding is a prerequisite for studying motion which will begin in earnest in the next chapter.
We will denote a vector quantity by a symbol with an arrow over the symbol, e.g., symbol for a position vector could be \(\vec r\text{.}\) The symbol stands for both the magnitude and direction. If we mean just the magnitude, we omit the overhead arrow from the symbol, e.g., we would write \(r \) for the magnitude of vector \(\vec r \text{,}\) \(v \) for the magnitude of vector \(\vec v \text{,}\) etc. The direction is usually given by angle(s) with respect to some reference direction(s) or just a description of the direction in space.
