Resultant Vector Homework: Min Value of |A+B+C|

Click For Summary
SUMMARY

The discussion focuses on calculating the minimum value of the resultant vector |A+B+C| given three vectors A, B, and C with magnitudes of 5, 6, and 7, respectively. The correct approach involves recognizing that the vectors can form the sides of a triangle, leading to a minimum resultant magnitude of zero when they are arranged optimally. The initial incorrect assumption of a minimum value of 4 was clarified through the understanding of vector cancellation and orientation.

PREREQUISITES
  • Understanding of vector addition and cancellation
  • Knowledge of vector magnitudes and directions
  • Familiarity with basic trigonometry
  • Concept of vectors forming triangles
NEXT STEPS
  • Study vector addition techniques in physics
  • Learn about the triangle inequality theorem in vector mathematics
  • Explore graphical representation of vectors and their resultant
  • Investigate advanced vector operations, such as dot and cross products
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector analysis and resultant calculations.

erisedk
Messages
372
Reaction score
7

Homework Statement


Three vectors A, B, C have magnitudes A=5, B=6 and C=7.
The minimum value of |A+B+C| is
*A represents magnitude, A represents the vector (magnitude and direction)

Homework Equations

The Attempt at a Solution


I got 4 because I think that the maximum possible cancellation occurring would be 7-(6+5). But it's wrong.
 
Physics news on Phys.org
Im not sure exactly how to approach this, i have a guess, but ill have to work on it. I am off to bed now, though. An example. Let the magnitude 6 vector point at 120 degrees. Let the 5 magnitude vector point at 60 degrees. Let the 7 vector point directly down. Whats the magnitude? Can you mathematically find a relationship between the vector components and their magnitudes?
 
I just figured it out, but thanks anyway. The three vectors can form the sides of a triangle, so the minimum will be zero.
 
  • Like
Likes   Reactions: scottdave

Similar threads

Replies
14
Views
2K
  • · Replies 4 ·
Replies
4
Views
6K
  • · Replies 18 ·
Replies
18
Views
1K
  • · Replies 20 ·
Replies
20
Views
12K
  • · Replies 6 ·
Replies
6
Views
2K
Replies
2
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 3 ·
Replies
3
Views
7K
  • · Replies 5 ·
Replies
5
Views
2K