Magnitude vs. Size: Understanding the Difference

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  • Thread starter Thread starter Bassel AbdulSabour
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Discussion Overview

The discussion focuses on the distinction between magnitude and size in the context of vectors, specifically addressing how a vector can have a magnitude expressed in Newtons while its representation on paper may be measured in centimeters. The scope includes conceptual clarification and technical explanation.

Discussion Character

  • Conceptual clarification, Debate/contested

Main Points Raised

  • Some participants propose that magnitude refers to the actual quantity of a vector (e.g., 9 Newtons), while size refers to its representation (e.g., 4 cm).
  • Others argue that the scale used to represent the vector can lead to confusion, suggesting that a scale of 9 N per 4 cm is not ideal and proposing alternatives like 1 cm = 2 N.
  • A participant questions the relevance of the size of the representation, emphasizing that the focus should be on the vector itself rather than how it is drawn.
  • Another participant agrees with the notion that the drawn length is immaterial to the vector's magnitude, reinforcing the distinction between the two concepts.

Areas of Agreement / Disagreement

Participants express differing views on the importance of the representation size versus the vector's magnitude, indicating that multiple competing perspectives remain unresolved.

Contextual Notes

Some assumptions about the definitions of magnitude and size are not explicitly stated, and the discussion does not resolve the implications of different scales for vector representation.

Bassel AbdulSabour
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What's the difference between magnitude and size? I mean, how can I say that AB vector has a magnitude of 9 Newton, and its length is 4 cm.
 
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I can see a reason for them to be different. Suppose one draws ##\vec{AB}## 4 cm long and that should represent 9 N, then you have a scale of ##{9 \over 4} ## N/cm. Then AB has a size of 4 cm and a magnitude of 9 N.
 
Bassel AbdulSabour said:
What's the difference between magnitude and size? I mean, how can I say that AB vector has a magnitude of 9 Newton, and its length is 4 cm.
You are trying to distinguish between the magnitude of a vector and the size of its representation drawn on a piece of paper? In my lifetime I have never heard anyone refer to the "size" of a vector in such a manner. Scientists, engineers and mathematicians are normally concerned with the vector, not with its representation.
 
jbriggs444 said:
You are trying to distinguish between the magnitude of a vector and the size of its representation drawn on a piece of paper? In my lifetime I have never heard anyone refer to the "size" of a vector in such a manner. Scientists, engineers and mathematicians are normally concerned with the vector, not with its representation.
I agree completely. The fact that the vector is drawn as one 4 cm. in length is immaterial -- its magnitude is 9 Nt.
 
Last edited:
4cm = 9N is a horrible scale. Why not 1cm = 2N?
 

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