Vectors and Scalars

Terms such as speed, velocity, distance, and displacement are used to describe the motion of an object. These quantities can be divided into two categories. Each one of these quantities is either a vector or a scalar:

Scalars are quantities that are fully described by a magnitude (or numerical value) alone. Vectors are quantities that are fully described by both a magnitude and a direction.

Examples of scalar quantities are:

• The mass has only a value, no direction
• The electric charge has only a value, no direction

Example of vector quantities:

• A force has a magnitude and a direction. You push or pull something with some strength (magnitude) in a particular direction.
• A velocity has a magnitude and a direction. An object that is moving always does so with a certain speed (magnitude) and in a particular direction.

Typographically, we may indicate that a variable is a vector by writing it in bold, adding an arrow on top of it, or both.

Vectors can also be represented by their coordinates.

Vector and scalar quantities are used in tensor analysis. They comprise a powerful mathematical tool that is used in many areas in engineering and physics.