## Two-Dimensional Vectors in Engineering |
## CHAPTER 4 |

The applications of two-dimensional vectors in engineering are introduced in this chapter. Vectors play a very important role in engineering. The quantities such as displacement (position), velocity, acceleration, forces, electric and magnetic fields, and momentum have not only a magnitude but also a direction associated with them. To describe the displacement of an object from its initial point, both the distance and direction are needed. A vector is a convenient way to represent both magnitude and direction and can be described in either a Cartesian or a polar coordinate system (rectangular or polar forms).

For example, an automobile traveling north at 65 mph can be represented by a two-dimensional vector in polar coordinates with a magnitude (speed) of 65 mph and a direction along the positive *y*-axis. It can also be represented by a vector in Cartesian coordinates with an *x*-component of zero and a *y*-component of 65 mph. The tip of the one-link and two-links planar robots introduced in Chapter 3 will be represented in this chapter using vectors both in Cartesian and polar coordinates. The concepts of unit vectors, magnitude, and direction of a vector will be introduced.

Graphically, a vector or simply with ...

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