Intersection points of the planes

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SUMMARY

The discussion focuses on finding the intersection points of the planes defined by the equations 2x - y - z = 3 and x + 2y + 3z = 7. The solution approach emphasizes that the intersection forms a line, and the first step is to determine the direction of this line. The participants agree that identifying the line's direction is the simplest method to solve the problem.

PREREQUISITES
  • Understanding of linear equations in three dimensions
  • Knowledge of vector direction and line representation
  • Familiarity with solving systems of equations
  • Basic skills in algebraic manipulation
NEXT STEPS
  • Study methods for solving systems of linear equations
  • Learn about vector representation of lines in 3D space
  • Explore techniques for finding intersection points of geometric planes
  • Investigate applications of linear algebra in geometry
USEFUL FOR

Students studying geometry, mathematics educators, and anyone interested in understanding the intersection of planes in three-dimensional space.

abs123456
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Homework Statement



Find all the intersection points of the planes:
2x-y-z=3
x+2y+3z= 7



Homework Equations



Whats the best n most simplest way to go about this question. Thanks

The Attempt at a Solution

 
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hi abs123456! :smile:
abs123456 said:
Whats the best n most simplest way to go about this question.

well, it's a line, so find the direction of the line first :wink:
 

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