Three vectors, of magnitudes 10 mm, 15 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant? a) O 15 mm b) O 20 mm c) O 65 mm d) O 85 mm
Three vectors, of magnitudes 10 mm, 15 mm and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant? a) O 15 mm b) O 20 mm c) O 65 mm d) O 85 mm
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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![**Question:**
Three vectors, of magnitudes 10 mm, 15 mm, and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?
a) 15 mm
b) 20 mm
c) 65 mm
d) 85 mm
**Explanation:**
When vectors are added together, the magnitude of the resultant vector can range from the absolute difference to the sum of the magnitudes of the individual vectors, depending on the angle between them.
- Minimum possible magnitude: \( |50 mm - (15 mm + 10 mm)| \) = 25 mm
- Maximum possible magnitude: \( 50 mm + 15 mm + 10 mm \) = 75 mm
Therefore, of the choices given, 65 mm is a possible magnitude for the resultant vector when the vectors are added together. The other options fall outside the calculated range of possibilities.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd1e4bb18-f27b-4648-9756-f50e39be2347%2Ff0ec47b9-bf2e-4440-b197-65de2961afc6%2Fbsx2d1s_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Question:**
Three vectors, of magnitudes 10 mm, 15 mm, and 50 mm, are added together. Which one of the following is a possible value for the magnitude of the resultant?
a) 15 mm
b) 20 mm
c) 65 mm
d) 85 mm
**Explanation:**
When vectors are added together, the magnitude of the resultant vector can range from the absolute difference to the sum of the magnitudes of the individual vectors, depending on the angle between them.
- Minimum possible magnitude: \( |50 mm - (15 mm + 10 mm)| \) = 25 mm
- Maximum possible magnitude: \( 50 mm + 15 mm + 10 mm \) = 75 mm
Therefore, of the choices given, 65 mm is a possible magnitude for the resultant vector when the vectors are added together. The other options fall outside the calculated range of possibilities.
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