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Finding the Intersection Point of a Third Plane

Finding the Intersection Point of a Third Plane
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2015-08-04 04:03
VectorCoordinate GeometrySolid Geometry
This example demonstrates how to determine the intersection point of three planes in space. Key math concepts include vectors, coordinate geometry, and solid geometry. GeoGebra commands and objects used are Vector, Intersect, Segment, Angle, and LaTeX for construction and display. Suitable for high school and above students learning spatial geometry.

GeoGebra Commands & Parameters

  1. Vector((1, 3, -2)) → n_1
  2. Vector((3, 5, -1)) → n_2
  3. IntersectPath(Π_1, Π_2) → L
  4. Intersect(Π_3, L) → P
  5. Segment(O, A) → a
  6. Segment(O, B) → b
  7. Segment(O, C) → c
  8. Angle(a, c) → α
  9. Angle(b, c) → β
  10. LaTeX(Π_1, true, true) → text1
  11. LaTeX(Π_2, true, true) → text2
  12. LaTeX(n_1, true, true) → text3
  13. LaTeX(n_2, true, true) → text4
  14. LaTeX(v, true, true) → text5
  15. LaTeX(L, true, true) → text6
  16. LaTeX(P, true, true) → text7
  17. LaTeX(Π_3, true, true) → text8