Trouble Understanding Geometric Algebra: Seeking Guidance

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Discussion Overview

The discussion revolves around understanding a specific example from the context of Geometric Algebra. Participants are addressing confusion regarding the reasoning presented in the example, seeking clarification on the problem and its solution.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Homework-related

Main Points Raised

  • Matheinste expresses confusion about the reasoning in the example and questions whether there is an error in the problem or solution.
  • Flux = Rad suggests converting the .doc file to a pdf to facilitate better responses from others.
  • Matheinste reiterates their confusion and questions their own understanding, asking if they are being foolish for not grasping the material.
  • Another participant asks for specifics about where Matheinste is lost in the example.
  • A participant provides a detailed explanation of the geometric reasoning involved, including the relationship between vectors and the conditions for perpendicularity, while also noting that their explanation aligns with the pdf file.
  • Matheinste later acknowledges a mistake in their understanding, attributing it to a slip in algebraic manipulation and misinterpreting a point as a vector, concluding that they were indeed confused.

Areas of Agreement / Disagreement

There is no consensus on the clarity of the example, as Matheinste initially expresses confusion while other participants assert that the reasoning is clear. The discussion reflects differing levels of understanding among participants.

Contextual Notes

Matheinste's confusion stems from a misunderstanding of the algebraic manipulation and the interpretation of geometric concepts, which may indicate a need for clearer definitions or explanations in the material.

matheinste
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This example appears in a set of notes entitled Geometric Algebra.

I cannot follow the first half of the example. Is the reasoning incorrect.

View attachment Doc1.doc

Thanks. Matheinste.
 
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A lot of people won't open your .doc file because it could potentially contain a virus. Try turning it into a pdf (there are loads of free sites online which will do this for you), you'll probably get a better response.
 
Thanks for the advice Flux = Rad.

View attachment Doc1.pdf

This appears in a set of files on the web making up a book called Geometric Algebra. Is there something wrong with the question or answer to the first problem or am I being stupid.

Matheinste.
 
Where, specifically, are you lost?
 
matheinste said:
This appears in a set of files on the web making up a book called Geometric Algebra. Is there something wrong with the question or answer to the first problem or am I being stupid.

I don't see anything wrong with the question or answer to the first problem.

I'm niot sure what you mean.
 
I have to agree with the others. It seems clear to me. Exactly where are you. You are given a line through O and x so that any point can be written as the vector xt for some number t. You are given a point y not on the line and asked to find t so that the line through y and tx is perpendicular to the original line.

Okay, the line segment from y to tx is given by y- tx and that must be perpendicular to x (I would have used "tx" but the vector from 0 to any point on that line, in particular x where t= 1 is parallel to tx and so perpendicular to any line perpendicular to tx)- their dot product must be 0: (y-tx). x= 0. Multiplying that out, y.x- t x.x= y.x- t|x||2= 0 (If we had used tx instead of x, we would now have ty.x- t2|x||2= t(y.x- t|x||2)= 0 and cancel that t leading to the same equation). Solving for t, t= y.x/||x||2. In particular the point is tx= (y.x/||x||2)x. To find the length, put that into ||y- tx||.

All I've really done is repeat what was said in your pdf file. If you need more, tell us what is confusing you.
 
Hello all. I see my mistake now, Just a basic slip in algebraic manipulationn and misinterpreting y as a point rather than a vector. So the answer to my question is yes--- I was being stupid.

Thanks Matheinste.
 

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