Skip to ContentGo to accessibility page
OpenStax Logo
University Physics Volume 1

Conceptual Questions

University Physics Volume 1Conceptual Questions

Conceptual Questions

2.1 Scalars and Vectors

1.

A weather forecast states the temperature is predicted to be −5°C−5°C the following day. Is this temperature a vector or a scalar quantity? Explain.

2.

Which of the following is a vector: a person’s height, the altitude on Mt. Everest, the velocity of a fly, the age of Earth, the boiling point of water, the cost of a book, Earth’s population, or the acceleration of gravity?

3.

Give a specific example of a vector, stating its magnitude, units, and direction.

4.

What do vectors and scalars have in common? How do they differ?

5.

Suppose you add two vectors A→A→ and B→B→. What relative direction between them produces the resultant with the greatest magnitude? What is the maximum magnitude? What relative direction between them produces the resultant with the smallest magnitude? What is the minimum magnitude?

6.

Is it possible to add a scalar quantity to a vector quantity?

7.

Is it possible for two vectors of different magnitudes to add to zero? Is it possible for three vectors of different magnitudes to add to zero? Explain.

8.

Does the odometer in an automobile indicate a scalar or a vector quantity?

9.

When a 10,000-m runner competing on a 400-m track crosses the finish line, what is the runner’s net displacement? Can this displacement be zero? Explain.

10.

A vector has zero magnitude. Is it necessary to specify its direction? Explain.

11.

Can a magnitude of a vector be negative?

12.

Can the magnitude of a particle’s displacement be greater than the distance traveled?

13.

If two vectors are equal, what can you say about their components? What can you say about their magnitudes? What can you say about their directions?

14.

If three vectors sum up to zero, what geometric condition do they satisfy?

2.2 Coordinate Systems and Components of a Vector

15.

Give an example of a nonzero vector that has a component of zero.

16.

Explain why a vector cannot have a component greater than its own magnitude.

17.

If two vectors are equal, what can you say about their components?

18.

If vectors A→A→ and B→B→ are orthogonal, what is the component of B→B→ along the direction of A→A→? What is the component of A→A→ along the direction of B→B→?

19.

If one of the two components of a vector is not zero, can the magnitude of the other vector component of this vector be zero?

20.

If two vectors have the same magnitude, do their components have to be the same?

2.4 Products of Vectors

21.

What is wrong with the following expressions? How can you correct them? (a) C=A→B→C=A→B→, (b) C→=A→B→C→=A→B→, (c) C=A→×B→C=A→×B→, (d) C=AB→C=AB→, (e) C+2A→=BC+2A→=B, (f) C→=A×B→C→=A×B→, (g) A→·B→=A→×B→A→·B→=A→×B→, (h) C→=2A→·B→C→=2A→·B→, (i) C=A→/B→C=A→/B→, and (j) C=A→/BC=A→/B.

22.

If the cross product of two vectors vanishes, what can you say about their directions?

23.

If the dot product of two vectors vanishes, what can you say about their directions?

24.

What is the dot product of a vector with the cross product that this vector has with another vector?

PreviousNext
Order a print copy
Citation/Attribution
Reuse and redistribution of this content in digital or print format:
  • This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's prior written permission.
  • This book uses the Creative Commons Attribution-NonCommercial-ShareAlike License, which means that you can reuse and modify the material only for noncommercial purposes, must attribute OpenStax, and must distribute any derivative works under the same license.
  • Any commercial printing of this textbook, including using a local or custom printer, must be approved by OpenStax, and proper citation provided.
  • OpenStax-copyrighted images, activities, assessments, and similar components of this book are subject to the same licensing – CC-BY-NC-SA. They can be used for noncommercial purposes with attribution. Commercial use requires permission.
  • Permission requests: Anyone who intends to incorporate this content (including text, images, and other components) into large language models, use it in AI offerings, use it commercially (including in print), and/or has questions about another use case is welcome to complete our reuse request form.
Attribution information
  • If you are redistributing all or part of this book in a noncommercial print format, then you must include on every physical page the following attribution:

    Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

  • If you are redistributing all or part of this book in a noncommercial digital format, then for every page that includes OpenStax content, you must license the derivative work under the same CC-BY-NC-SA license as the original, and include on every digital page view the following attribution:

    Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction

Citation information

The information below includes the information needed to generate citations in most major styles (APA, MLA, etc.); you must reformat and organize the information as needed to fit the requirements of the style. Use the information below to generate a citation. We recommend using a citation tool such as this one.

© Jun 11, 2026 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo, and Rice University name, and Rice University logo trademarks, or wordmarks are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.