How to find the canonical form of a straight line equation in space?

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Discussion Overview

The discussion revolves around the process of converting the general equation of a line in space, defined by two intersecting planes, into its canonical form. Participants seek clarification on the definitions and methods involved, as well as the necessary references for the equations being discussed.

Discussion Character

  • Debate/contested
  • Homework-related

Main Points Raised

  • One participant asks how to change the general equation of a line in space into canonical form, indicating a lack of clarity on the topic.
  • Several participants request the specific general equation and the definition of the canonical form to provide more targeted assistance.
  • Another participant mentions the general form of the line equation is derived from two intersecting planes but does not provide the equations of those planes.
  • A participant references a similar problem involving specific plane equations and asks for a discussion on the solution, suggesting a connection to the original question.
  • One participant expresses frustration over the lack of provided information and suggests that the inquiry may belong in a homework forum, emphasizing the need for a complete context and attempts at a solution.
  • There is a suggestion to use LaTeX for presenting equations to facilitate clearer communication.

Areas of Agreement / Disagreement

Participants do not reach a consensus, as there is disagreement on the adequacy of the information provided and the appropriateness of the forum for the discussion. Multiple views on how to proceed with the inquiry remain unresolved.

Contextual Notes

The discussion lacks specific equations and references, which are necessary for a thorough exploration of the topic. There is also uncertainty regarding whether the inquiry is a homework problem, which affects the context of the discussion.

AhmedHesham
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Hi friends
How exactly do we change the general equation of a line in space( given two intersecting planes) into the canonical form
Thanks
 
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What general equation are you starting from, and what do you think the canonical form is?

A reference would be helpful.
 
PeterDonis said:
What general equation are you starting from, and what do you think the canonical form is?

A reference would be helpful.
I am talking in general
The general form of equation of line in space is given by two intersecting planes
We have the equations of the two planes
How do we formulate the equation of the line in the canonical form
The reference is my school book
 
AhmedHesham said:
We have the equations of the two planes

So what are they?

AhmedHesham said:
How do we formulate the equation of the line in the canonical form

What is the canonical form?

AhmedHesham said:
The reference is my school book

We don't know what book that is. Please give an explicit reference.
 
We have two equations
Each one representing a plane in 3d space
8] Find the equation of line 2 x - 3 y + 6 z + 1 = 0,
5x +5y – 7z - 11=0 in parametric form then find the point of
intersection of this line with the plane x+y+2z=0.This is the statement of another similar problem if you don't know what the canonical means
Let us discuss the solution
 
AhmedHesham said:
Let us discuss the solution

No, let us close this thread since you have not provided the information needed to discuss anything.

Also, if this is a homework problem, which I strongly suspect it is, it belongs in the homework forum, not here, and if you want to start a new thread on it there, you will need to fill out the homework template, which requires you to give all relevant equations and also to give your attempt at a solution.

Finally, when giving equations here, please use the PF LaTeX feature. The "LaTeX Guide" link at the bottom left of the edit window will take you to a help page on that.
 
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