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1. Two vectors A and B have fixed magnitudes but their ori A+B B

1. Two vectors A and B have fixed magnitudes but their ori A+B B

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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# Vectors and Their Resultant Magnitudes ## Problem Statement 1. **Two vectors A and B have fixed magnitudes, but their orientations can be changed.** A diagram illustrates two vectors, A and B, arranged tip-to-tail. Vector A is along a set path, and vector B can be rotated to form different angles with A. The resultant vector, A + B, is shown as a dashed arrow from the tail of A to the tip of B. ### Question If the vectors are arranged tip-to-tail and you rotate vector B, what should the angle between vectors A and B be so that: #### (a) The resultant of A + B has the **maximum magnitude**? - [X] 0° - [ ] 45° - [ ] 90° - [ ] 180° #### (b) The resultant of A + B has the **minimum magnitude**? - [ ] 0° - [ ] 45° - [ ] 90° - [X] 180° ### Explanation - **Maximum Magnitude:** The magnitude of the resultant vector A + B is maximum when the two vectors are aligned in the same direction (angle = 0°). - **Minimum Magnitude:** The magnitude of the resultant vector A + B is minimum when the two vectors are aligned in opposite directions (angle = 180°).
Transcribed Image Text:# Vectors and Their Resultant Magnitudes ## Problem Statement 1. **Two vectors A and B have fixed magnitudes, but their orientations can be changed.** A diagram illustrates two vectors, A and B, arranged tip-to-tail. Vector A is along a set path, and vector B can be rotated to form different angles with A. The resultant vector, A + B, is shown as a dashed arrow from the tail of A to the tip of B. ### Question If the vectors are arranged tip-to-tail and you rotate vector B, what should the angle between vectors A and B be so that: #### (a) The resultant of A + B has the **maximum magnitude**? - [X] 0° - [ ] 45° - [ ] 90° - [ ] 180° #### (b) The resultant of A + B has the **minimum magnitude**? - [ ] 0° - [ ] 45° - [ ] 90° - [X] 180° ### Explanation - **Maximum Magnitude:** The magnitude of the resultant vector A + B is maximum when the two vectors are aligned in the same direction (angle = 0°). - **Minimum Magnitude:** The magnitude of the resultant vector A + B is minimum when the two vectors are aligned in opposite directions (angle = 180°).
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