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Line and Plane Position Relationship (GeoGebra)

Line and Plane Position Relationship (GeoGebra)
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2017-11-09 17:07
VectorCoordinate GeometrySolid GeometryGeometric Construction
This GeoGebra example demonstrates the positional relationship between a line and a plane in three-dimensional space, including cases of intersection, parallelism, and perpendicularity. Core mathematical concepts involve three-dimensional analytic geometry, vector operations, intersection point calculation, and distance formulas. Construction utilizes GeoGebra commands such as Cube, Plane, Line, Intersect, Vector, OrthogonalVector, Segment, and Distance to build a cube model with labeled faces and edges. Suitable for high school three-dimensional geometry lessons or introductory university space geometry, helping learners visually understand and compute the relative position of a line and a plane.

GeoGebra Commands & Parameters

  1. Cube(A, B, C) → a, D, FlächeCDHG, FlächeEFGH, KanteAD, KanteAB, KanteBC, KanteCD, KanteAE, KanteDH, KanteEH, KanteEF, E, KanteBF, KanteFG, KanteCG, KanteGH, F, G, H, FlächeABCD, FlächeADHE, FlächeABFE, FlächeBCGF
  2. Polygon(B, F, G, C) → v2, b, f_1, g, c
  3. PointIn(v2) → J
  4. Polygon(A, E, H, D) → v1, a_1, e, h, d
  5. PointIn(v1) → I
  6. Line(round((I * 100)) / 100, round((J * 100)) / 100) → f
  7. Point(KanteAE) → K
  8. Point(KanteBF) → L
  9. Point(KanteCG) → Q
  10. Plane(round((K * 100)) / 100, round((L * 100)) / 100, round((Q * 100)) / 100) → i
  11. Intersect(f, i) → S
  12. Intersect(zAxis, xAxis) → M
  13. Point(xAxis) → N
  14. Vector(M, N) → u
  15. Point(yAxis) → O
  16. Vector(M, O) → v
  17. Point(zAxis) → P
  18. Vector(M, P) → w
  19. PointIn(i) → T
  20. OrthogonalVector(i) → j
  21. Intersect(i, Segment[A, D]) → U1
  22. Intersect(i, Segment[C, D]) → U2
  23. Intersect(i, Segment[H, D]) → U3
  24. Segment(K, L) → m
  25. Segment(L, Q) → n
  26. Segment(Q, U2) → p
  27. Segment(U2, U1) → q
  28. Segment(U1, K) → r
  29. Segment(Q, U3) → s
  30. Segment(U3, K) → t
  31. Distance(S, S) → SS
  32. Intersect(i, KanteGH) → U4
  33. Intersect(i, KanteEH) → U5
  34. Segment(Q, U4) → g_1
  35. Segment(U4, U5) → h_1
  36. Segment(U5, K) → i_1
  37. Point(f) → U

AI Drawing Prompt Reference

Draw a cube with all faces and edges. Then take two points on one edge and draw a line through them. Next, construct a plane using three edges of the cube as base points. This line intersects the plane at one point. Finally, calculate the angle between the line and the plane, and mark all key points and segments.
The prompt above was compiled from the original drawing commands and is for reference only.