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Find a Line Parallel to Two Planes

Find a Line Parallel to Two Planes
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2015-08-04 02:59
VectorCoordinate GeometrySolid Geometry
This example demonstrates how to find a line that is parallel to two given planes. Key mathematical concepts include plane equations and vectors. Using GeoGebra commands such as Vector, IntersectPath, and Line, the construction of the required line is shown. Suitable for high school mathematics education or students learning coordinate geometry.

GeoGebra Commands & Parameters

  1. Vector((3, -1, 1)) → n
  2. Vector((1, 2, -1)) → m
  3. IntersectPath(Π_1, Π_2) → a
  4. Vector(P, (8.3636, -1.4545, 1.4545)) → n_1
  5. Vector(P, (6.3636, 1.5455, -0.5455)) → n_2
  6. Vector(P, (4.3636, 3.5455, 7.4545)) → v
  7. Line(M, v) → L
  8. LaTeX(Π_1, true, true) → text1
  9. LaTeX(Π_2, true, true) → text2
  10. LaTeX(M, true, true) → text3
  11. LaTeX(n_1, true, true) → text4
  12. LaTeX(n_2, true, true) → text5
  13. LaTeX(v, true, true) → text6
  14. LaTeX(L, true, true) → text7
  15. Angle(n_1, n_2) → α
  16. Angle(n_1, v) → β
  17. Angle(n_2, v) → γ