Chapter 2 · Vectors CHAPTER 3 · Particle Equilibrium →

Vector Overview

Many quantities in statics can be described by a single number, while others require both a magnitude and a direction. In this section we distinguish between scalars and vectors and look at common ways of writing vector quantities.

Scalars

Scalars are quantities that are fully described by a single number representing their magnitude. They have no associated direction. Typical scalar quantities in mechanics include:

Time

Clock representing time

Temperature

Thermometer representing temperature

Mass

Mass block representing mass

Vectors

Vectors are distinct from scalars because they have both magnitude and direction. A vector describes not only “how much” but also “where”.

Force

Force represented as a vector

Velocity

Velocity represented as a vector

Graphical Representation of a Vector

Vectors are often represented as arrows: the length of the arrow corresponds to the magnitude, and the arrowhead indicates the direction.

Vector represented as an arrow showing tail, head, magnitude, and direction angle theta

Common Notations for Vectors

Vectors can be represented in several notational styles:

  • Bold font (e.g., \(\mathbf{A}\)) – commonly used in typed or printed documents to distinguish vectors from scalars.
  • Arrow above the letter (e.g., \(\vec{A}\)) – a standard representation in physics and engineering texts.
  • Line above or below the letter (e.g., \(\overline{A}\) or \(\underline{A}\)) – frequently used in example problems or handwritten notes when boldface is not convenient.