Calculating Work Between Two Points on a Line – Simple Question

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Discussion Overview

The discussion revolves around calculating the work done between two points on a line, specifically points A(1, 0, 0) and B(0, 1, (pi^3)/8). Participants are examining the parametric equation of the line connecting these points and clarifying the formulation of the position vector.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant presents a parametric equation for the line connecting points A and B, questioning its correctness and expressing uncertainty about its derivation.
  • Another participant confirms that the equation represents the parametric form of the line and explains how varying the parameter t yields different points along the line.
  • A participant seeks clarification on the correctness of the equation, specifically questioning the presence of the term -i.
  • Another participant supports the original equation, demonstrating that substituting t = 0 and t = 1 yields the correct points A and B, respectively.
  • One participant expresses confusion about how to derive the position vector from the two points.
  • A later reply clarifies that the vector from point B to point A can be found by subtracting the position vector of A from that of B.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correctness of the initial parametric equation, as some express uncertainty and seek clarification while others affirm its validity.

Contextual Notes

Participants discuss the formulation of the position vector and the implications of the parametric equation without resolving the underlying assumptions or potential typos in the original equation.

Master J
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Simple question.

So in an example question I'm lookin at finding the work between 2 points on a line.

The points are A(1, 0, 0) and B(0, 1, (pi^3)/8)

The vector of the line joining these points is then given as:

r = i + t(-i + j + [(pi^3)/8]k )


Is that correct? I can't see how that equation arises? It could just be a typo, or I'm just having a stupid day!

Cheers!
 
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No, that's the parametric equation of the (straight) line connecting those points. Taking different values of t in the range [0,1] gives you different points along that line.
 
Yes, but is it correct? Shud there be a -i in there?

Is it r = a + tb ?
 
It looks OK to me. Substitute t = 0 and you get point A. Substitute t = 1 and you get point B. In unit vector notation,

[tex]\vec A = 1 \hat i + 0 \hat j + 0 \hat k[/tex]

[tex]\vec B = 0 \hat i + 1 \hat j + \frac{\pi^3}{8} \hat k[/tex]
 
I guess I'm confused as to that vector. How do you make that position vector from those 2 points?
 
The vector from B to A is simply
[tex]\vec{B} - \vec{A}[/tex]
 

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