Linear algebra, parametric equation, intersectin of line

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Homework Help Overview

The problem involves finding the parametric equation for the line of intersection of two planes in three-dimensional space, represented by the equations 2x+y-2z=1 and x-2y+z=-3.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to use Gauss-Jordan elimination to solve the system of equations and expresses the intersection in parametric form. Some participants confirm the correctness of the parametric equations derived, while others question whether additional forms, such as vector representation, are required.

Discussion Status

The discussion reflects a mix of confirmations regarding the parametric equations and some uncertainty about whether further steps are necessary. Participants are clarifying the requirements of the problem and exploring interpretations of the task.

Contextual Notes

There is some confusion regarding the nature of the problem, with participants questioning if a specific type of intersection line needs to be identified beyond the parametric form provided.

cleopatra
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Homework Statement



Two equations for two planes in 3-D
2x+y-2z=1
x-2y+z=-3
Find the parametric equation for the line of intersection of the two planes by solving these two equations togeather.

The Attempt at a Solution



Gauss Jordan gives:
1 0 -3/5 -1/5
0 1 -4/5 7/5

if z=t
x=3/5t-1/5
y=4/5t+7/5

I don´t know how to finish the problem.
 
Last edited:
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You have already solved the problem!

x=3/5t-1/5
y=4/5t+7/5
z=t

is the parametric equation for the intersection.
 
Last edited:
You are already finished. z=t, x=(3/5)t-1/5 and y=(4/5)t+7/5 is the intersection line in parametric form. Are you supposed to express it in vector form or something?
 
really? I thought this was only the parametric equation and I had to find some special line of intersection as well.
 
cleopatra said:
really? I thought this was only the parametric equation and I had to find some special line of intersection as well.

Nah. The problem says find the line that is the intersection of the two planes. No line intersection involved.
 
okey thanks for that
 

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