Vector Properties: Does Length Affect Components?

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Discussion Overview

The discussion revolves around the properties of vectors, specifically whether the length of a vector affects its components as the vector approaches zero length. Participants explore the implications of this limit in the context of vector components.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions whether it is correct to assume that if the length of a vector approaches 0, then any component of that vector must also approach 0.
  • Another participant agrees with this assumption and references a proof they believe supports it, although the details of the proof are not provided.
  • A third participant reiterates the agreement but emphasizes that it is against forum rules to provide direct answers without encouraging the original poster to calculate limits independently.
  • Some participants express concern about the appropriateness of the question's placement in the forum, clarifying that it was not intended as a homework question but rather a personal inquiry.

Areas of Agreement / Disagreement

There is some agreement among participants regarding the assumption that vector components approach zero as the vector length approaches zero. However, there is contention regarding the manner of responding to the original question and the appropriateness of the forum section for such inquiries.

Contextual Notes

Participants note potential limitations in the clarity of the original question and the implications of the assumptions made about vector components and their limits.

nuuskur
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Is there something said about [itex]\lim_{||v||\to 0} \frac{v_i}{||v||}[/itex]? Is it correct to assume if the length of a vector approaches 0, then any component of that vector has to approach 0, aswell?
 
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I would say yes... check out the proof I did... which I think works.. and similarily with substituting into y.
 

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DannyMoretz said:
I would say yes... check out the proof I did... which I think works.. and similarily with substituting into y.
It is against the rules at PF to give answers like that. You should've asked the OP to calculate the limits himself/herself.
 
I didn't post this in a homeworks' section and it isn't one, either. I was merely curious and couldn't find relevant info on it myself, since my English is bad.
 
nuuskur said:
I didn't post this in a homeworks' section and it isn't one, either. I was merely curious and couldn't find relevant info on it myself, since my English is bad.
Sorry, I didn't pay attention to the section. But I wanted to mention it to Danny, who is new here. It would still have been better to start by pointing you in the right direction.
 

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