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

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SUMMARY

The discussion focuses on converting the general equation of a line in space, defined by two intersecting planes, into its canonical form. Participants emphasize the need for specific equations of the planes to provide a meaningful response. A problem involving the equations of two planes, 2x - 3y + 6z + 1 = 0 and 5x + 5y - 7z - 11 = 0, is mentioned as a reference for understanding the canonical form. The conversation highlights the importance of providing explicit references and details when seeking assistance with mathematical problems.

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  • Understanding of linear equations in three-dimensional space
  • Familiarity with the concept of canonical forms in geometry
  • Knowledge of parametric equations
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  • Study the derivation of canonical forms for lines in 3D space
  • Learn how to convert general equations of planes into parametric forms
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Students studying geometry, mathematics educators, and anyone seeking to understand the conversion of line equations in three-dimensional space.

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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