Physics
Textbooks
Boundless Physics
Kinematics
Basics of Kinematics
Physics Textbooks Boundless Physics Kinematics Basics of Kinematics
Physics Textbooks Boundless Physics Kinematics
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 6
Created by Boundless

Introduction to Scalars and Vectors

A vector is any quantity that has both magnitude and direction, whereas a scalar has only magnitude.

Learning Objective

  • Distinguish the difference between scalars and vectors


Key Points

    • A vector is any quantity that has magnitude and direction.
    • A scalar is any quantity that has magnitude but no direction.
    • Displacement and velocity are vectors, whereas distance and speed are scalars.

Terms

  • vector

    A directed quantity, one with both magnitude and direction; the between two points.

  • scalar

    A quantity that has magnitude but not direction; compare vector.


Example

    • A person's speed can stay the same as he or she rounds a corner and changes direction. Given this information, is speed a scalar or a vector quantity? Speed is a scalar quantity. It does not change at all with direction changes; therefore, it has magnitude only. If it were a vector quantity, it would change as direction changes (even if its magnitude remained constant).

Full Text

What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined by magnitude alone. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector is any quantity with both magnitude and direction. Other examples of vectors include a velocity of 90 km/h east and a force of 500 newtons straight down.

Scalars and Vectors

Mr. Andersen explains the differences between scalar and vectors quantities. He also uses a demonstration to show the importance of vectors and vector addition.

In mathematics, physics, and engineering, a vector is a geometric object that has a magnitude (or length) and direction and can be added to other vectors according to vector algebra. The direction of a vector in one-dimensional motion is given simply by a plus (+) or minus (−) sign. A vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B, as shown in .

Vector representation

A vector is frequently represented by a line segment with a definite direction, or graphically as an arrow, connecting an initial point A with a terminal point B.

Some physical quantities, like distance, either have no direction or no specified direction. In physics, a scalar is a simple physical quantity that is not changed by coordinate system rotations or translations. It is any quantity that can be expressed by a single number and has a magnitude, but no direction. For example, a 20ºC temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km/h speed limit, a person's 1.8 m height, and a distance of 2.0 m are all scalars, or quantities with no specified direction. Note, however, that a scalar can be negative, such as a −20ºC temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows. (A comparison of scalars vs. vectors is shown in . )

Scalars vs. Vectors

A brief list of quantities that are either scalars or vectors.

[ edit ]
Edit this content
Prev Concept
Reference Frames and Displacement
Average Velocity: A Graphical Interpretation
Next Concept
Subjects
  • Accounting
  • Algebra
  • Art History
  • Biology
  • Business
  • Calculus
  • Chemistry
  • Communications
  • Economics
  • Finance
  • Management
  • Marketing
  • Microbiology
  • Physics
  • Physiology
  • Political Science
  • Psychology
  • Sociology
  • Statistics
  • U.S. History
  • World History
  • Writing

Except where noted, content and user contributions on this site are licensed under CC BY-SA 4.0 with attribution required.