Vector

Exercise of vector

Certain physical quantities are fully described by a single number: for example, the mass of a stone, the speed of a car. Such quantities are called scalars. On the other hand, some quantities are not fully described until a direction is specified in addition to the number. For example, a velocity of 30 meters per second due east is different from a velocity of 30 meters per second due north. These quantities are called vectors and it is important to distinguish them from scalars. There are many engineering applications in which vector and scalar quantities play important roles. For example, speed, potential, work and energy are scalar quantities, while velocity, electric and magnetic forces, the position of a robot and the state-space representation of a system can all be described by vectors. A variety of mathematical techniques have been developed to enable useful calculations to be carried out using vectors and in this chapter these will be discussed