Scalars and Vectors

Definitions

Scalars are quantities that are fully described by a single number, representing their magnitude. Examples of scalar quantities include:

Time



Temperature



Mass

Vectors are distinct from scalars because they have both magnitude and direction. This means they describe not only how much (magnitude) but also where (direction). Vectors are often represented as arrows, with the length of the arrow corresponding to the magnitude and the arrowhead indicating the direction.

Force



Velocity

Common Notations for Vectors

Vectors can be represented in several ways:

• Bold font (e.g., \(\mathbf{A}\)) – Often used in typed or printed documents to distinguish vectors from scalars.
• Arrow above the letter (e.g., \(\vec{A}\)) – A common 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.