Equation of plane containing the intersection of two planes

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Homework Help Overview

The problem involves finding an equation of a plane that passes through a specific point and contains the line of intersection of two given planes. The subject area relates to vector geometry and the equations of planes in three-dimensional space.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to derive the equation of the plane using the normal vectors of the given planes and the point through which the plane must pass. Some participants question the correctness of the original poster's approach and the validity of the textbook's solution.

Discussion Status

The discussion is ongoing, with participants exploring the correctness of the original poster's solution and considering alternative methods to verify the results. There is no explicit consensus on the accuracy of the answers provided.

Contextual Notes

Participants note that the textbook may contain errors, which raises questions about the reliability of the provided solution. The original poster is seeking clarification on their approach and the validity of their results.

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Homework Statement


Find an equation of the plane that passes through the point (-1,2,1) and contains the line of intersection of the planes x + y - z = 2 and 2x - y + 3z = 1




Homework Equations


Equation of a plane:
a(x-x0) + b(y-y0) + c(z-z0) = 0


The Attempt at a Solution


n1 = <1,1,-1>
n2 = <2,-1,3>
n1[tex]\times[/tex]n2 = <2,-5,-3> = <a,b,c>

Equation:
2(x+1) - 5(y-2) - 3(z-1) = 0
2x - 5y - 3z = -15

What am I doing wrong? Any help is appreciated.
 
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What makes you think you are doing anything wrong?
 
The solutions section in the back of my textbook says the answer is x - 2y + 4z = -1.
My textbook occasionally has wrong answers, though. So my answer is OK?
 
Looking at it quickly, it looks right to me. But if you want to be absolutely certain, you could determine a couple of points on the intersection of the planes by using their equations. Then if those two points are on your proposed plane the whole line of intersection must be and you are certain.
 

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