Finding Equation of line of intersecting planes

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SUMMARY

The discussion focuses on determining the equation of a line formed by the intersection of two planes in three-dimensional space. The direction vector of the line is calculated using the cross product of the normal vectors of the intersecting planes. To find a specific point on the line of intersection, denoted as r₀, one must identify a point that satisfies the equations of both planes simultaneously.

PREREQUISITES
  • Understanding of vector mathematics, specifically cross products.
  • Familiarity with the equations of planes in three-dimensional space.
  • Knowledge of parametric equations of lines.
  • Basic skills in solving systems of equations.
NEXT STEPS
  • Study vector cross product calculations in detail.
  • Learn how to derive the equations of planes from given points and normal vectors.
  • Explore methods for finding intersection points of geometric shapes in three dimensions.
  • Investigate parametric equations and their applications in line representation.
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Students and professionals in mathematics, physics, and engineering who are working with three-dimensional geometry and need to understand the intersection of planes and lines.

Larrytsai
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Hey guys,

I just have a general question, How would you find the equation of a line with just the equations of the planes intersecting. I know for the direction vector it would be the cross product, but for the other part of the equation r=ro +tv, the ro part i do not know how to find.
 
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[tex]r_0[/tex] is any single point on the line of intersection, which means you just need to find anyone point that lies on both planes.
 

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