How Do You Find the Line of Intersection Between Two Planes?

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SUMMARY

The discussion focuses on finding the line of intersection between two planes defined by the equations z = x + y (Plane 1) and 2x - 5y - 2z = 1 (Plane 2). By substituting z from Plane 1 into the equation of Plane 2, users can derive a linear equation involving only x and y. This approach simplifies the problem, allowing for the determination of the intersection line as a straight line in the xy-plane.

PREREQUISITES
  • Understanding of linear equations and their graphical representation
  • Familiarity with substitution methods in algebra
  • Basic knowledge of three-dimensional geometry
  • Ability to manipulate equations with multiple variables
NEXT STEPS
  • Study the method of solving systems of equations using substitution
  • Learn about the geometric interpretation of lines and planes in three-dimensional space
  • Explore the concept of parametric equations for lines in 3D
  • Investigate the use of software tools like GeoGebra for visualizing intersections of planes
USEFUL FOR

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

Scharles
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Given :
plane 1 : z=x+y
plane 2 : 2x-5y-2z=1

Find the equation of intersection of plane 1 and plane 2.

i have no idea how to solve 3 unknowns in 2 quations, please help~ thanks~
 
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Simply substitute z=x+y to equation of plane 2 and you ll have an equation involving only x and y to the first order, so it will be the equation of a streight line.
 

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