Finding distance between vectors

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Discussion Overview

The discussion revolves around determining the distance between two vectors, $\vec{A}$ and $\vec{B}$, expressed in cylindrical coordinates. Participants explore the implications of the question and the appropriate methods to approach it.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the validity of the question, stating that vectors do not have a fixed position and thus cannot have a distance between them.
  • Another participant suggests that the problem might be interpreted as finding the distance from point A (represented by vector $\vec{A}$) to point B (represented by vector $\vec{B}$).
  • A further suggestion is made to convert the cylindrical coordinates of the vectors into Cartesian coordinates to apply the standard distance formula.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the interpretation of the question, with some viewing it as nonsensical while others propose methods to find a distance between the points represented by the vectors.

Contextual Notes

Assumptions about the coordinate system and the interpretation of vectors are not fully resolved, and the discussion reflects differing views on the nature of vectors and distances.

Drain Brain
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Given $\vec{A}=2.15a\rho+6.25a\phi+3az$ and $\vec{B}=0.11a\rho+3.35a\phi+2az$. Determine the distance from $\vec{A}$ to $\vec{B}$.


what to do first?
 
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This question doesn't make a whole lot of sense. I am assuming you are dealing with a cylindrical polar orthonormal system, which is fine. But there is no such thing as finding "distances between vectors", because vectors do NOT have any position! All they have is direction and magnitude. That is why they can be picked up and moved anywhere you like.
 
maybe the problem is asking about a vector from A to B.
How can I do that?
 
You can convert cylindrical coordinates to Cartesian coordinates and use the standard formula for distance.
 

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