Vectors In Two Dimensions
Overview
A vector carries both size and direction, making it the natural language for displacement, velocity and force. In two dimensions you can add, subtract and scale vectors, and find a magnitude using Pythagoras.
In this lesson you will use vector notation, position vectors and unit vectors, find the magnitude of a vector, and add, subtract and multiply vectors by scalars.
Objectives
- Understand and use vector notation, position vectors and unit vectors.
- Find the magnitude of a vector; add and subtract vectors and multiply a vector by a scalar.
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Lesson Note
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Lesson Evaluation
Congratulations on completing the lesson on Vectors In Two Dimensions. Now that you've explored the key concepts and ideas, it's time to put your knowledge to the test. This section offers a variety of practice questions designed to reinforce your understanding and help you gauge your grasp of the material.
You will encounter a mix of question types, including multiple-choice questions, short answer questions, and essay questions. Each question is thoughtfully crafted to assess different aspects of your knowledge and critical thinking skills.
Use this evaluation section as an opportunity to reinforce your understanding of the topic and to identify any areas where you may need additional study. Don't be discouraged by any challenges you encounter; instead, view them as opportunities for growth and improvement.
- If a = (4, 1) and b = (1, 3), then a + b =: A. (5, 4) B. (4, 3) C. (3, -2) D. (5, 3) Answer: A
- If a = (4, 1) and b = (1, 3), then a - b =: A. (5, 4) B. (3, -2) C. (-3, 2) D. (3, 2) Answer: B
- The magnitude of (5, 4) is: A. 9 B. √41 C. 20 D. 41 Answer: B
- A unit vector has magnitude: A. 0 B. 1 C. 2 D. its length Answer: B
- Vector addition follows the: A. triangle law B. circle law C. square law D. inverse law Answer: A
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Recommended Books
Further learning from open sources
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Textbook section
Vectors
View vectors geometrically.
"Algebra and Trigonometry: Vectors" by OpenStax, OpenStax, Rice University, licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). Source: https://openstax.org/books/algebra-and-trigonometry/pages/10-8-vectors. Access for free at https://openstax.org/books/algebra-and-trigonometry/pages/1-introduction
Published by other organisations under open licences, credited as they ask. Links open their websites.
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