When magnitude of addition is equals to

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Discussion Overview

The discussion revolves around the relationship between the magnitudes of the sum and difference of two vectors, specifically questioning why these magnitudes being equal implies that the angle between the vectors is 90 degrees. The inquiry seeks explanations and mathematical reasoning behind this concept.

Discussion Character

  • Exploratory
  • Mathematical reasoning

Main Points Raised

  • One participant asserts that when the magnitude of the addition of two vectors equals the magnitude of their difference, the angle between them must be 90 degrees, seeking clarification on this assertion.
  • Another participant prompts for a sketch and suggests expressing the magnitudes of the sum and difference in terms of the vectors' individual magnitudes and the angle between them.
  • A further contribution encourages consideration of the scalar (dot) product of the two vectors and its relation to the equality of the magnitudes of the sum and difference.

Areas of Agreement / Disagreement

The discussion does not appear to reach a consensus, as participants are exploring the implications and mathematical relationships without settling on a definitive explanation.

Contextual Notes

Participants have not provided specific assumptions or definitions that may be necessary for a complete understanding of the problem, and there are unresolved mathematical steps in the reasoning process.

H.D. M A K
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When magnitude of addition is equals to the magnitude of difference of two vectors then the angle between them will be 90 degrees... How and Why ? can anyone explain it ??
Any help will be appreciated..
Thanks
 
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Did you draw a sketch? Can you express the magnitude of the sum and the difference in terms of their individual magnitudes and the angle?
 
H.D. M A K said:
When magnitude of addition is equals to the magnitude of difference of two vectors then the angle between them will be 90 degrees... How and Why ? can anyone explain it ??
Any help will be appreciated..
Thanks

Think about two vectors: (a1, b1, c1, ...) and (a2, b2, c2, ...)
What are the magnitudes of the sum and difference of these two vectors? Set these two equations equal to each other and simplify.
What is the scalar (dot) product of the two vectors? How is this related to the result from the first part?
 
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