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Intersection of Planes Demo

Intersection of Planes Demo
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2017-09-15 09:52
VectorFunctionCoordinate GeometrySolid Geometry
This example demonstrates the intersection of three planes in 3D space. Key math concepts include plane equations, 3D analytical geometry, vector cross product, and linear combinations. GeoGebra commands and objects used in construction include IntersectPath (for intersection calculations), FractionText (for fraction display), TableText (for tabular text), Segment (for line segment drawing), RotateText (for text rotation), and Textfield (for text input). Suitable for high school students and math enthusiasts to understand plane intersections in solid geometry and linear algebra.

GeoGebra Commands & Parameters

  1. IntersectPath(a, b) → j
  2. IntersectPath(b, c) → k
  3. IntersectPath(a, c) → l
  4. IntersectPath(a, d) → m
  5. IntersectPath(a, e) → p
  6. IntersectPath(d, e) → q
  7. IntersectPath(d, f) → r
  8. IntersectPath(d, g) → s
  9. IntersectPath(f, g) → t
  10. IntersectPath(h, i) → a_1
  11. IntersectPath(h, n) → b_1
  12. IntersectPath(i, n) → c_1
  13. FractionText(B6) → text6
  14. FractionText(C6) → text7
  15. FractionText(E6) → text8
  16. TableText({{A2, B2, C2}}, "|_") → text12
  17. TableText({{A3, B3, C3}}, "|_") → text13
  18. TableText({{A4, B4, C4}}, "|_") → text14
  19. TableText({{E2}}, "|_") → text15
  20. TableText({{E3}}, "|_") → text16
  21. TableText({{E4}}, "|_") → text17
  22. TableText({{A6, B6, C6}}, "|_") → text18
  23. TableText({{A7, B7, C7}}, "|_") → text19
  24. TableText({{A8, B8, C8}}, "|_") → text20
  25. TableText({{E10}}, "|_") → text21
  26. TableText({{E11}}, "|_") → text22
  27. TableText({{E12}}, "|_") → text23
  28. TableText({{E6}}, "|_") → text24
  29. TableText({{E7}}, "|_") → text25
  30. TableText({{E8}}, "|_") → text26
  31. TableText({{A10, B10, C10}}, "|_") → text27
  32. TableText({{A11, B11, C11}}, "|_") → text28
  33. TableText({{A12, B12, C12}}, "|_") → text29
  34. TableText({{A14, B14, C14}}, "|_") → text34
  35. TableText({{A15, B15, C15}}, "|_") → text35
  36. TableText({{A16, B16, C16}}, "|_") → text36
  37. TableText({{E14}}, "|_") → text37
  38. TableText({{E15}}, "|_") → text38
  39. TableText({{E16}}, "|_") → text39
  40. TableText({{A18, B18, C18}}, "|_") → text42
  41. TableText({{A19, B19, C19}}, "|_") → text43
  42. TableText({{A20, B20, C20}}, "|_") → text44
  43. TableText({{E18}}, "|_") → text45
  44. TableText({{E19}}, "|_") → text46
  45. TableText({{E20}}, "|_") → text47
  46. TableText({{A22, B22, C22}}, "|_") → text48
  47. TableText({{A23, B23, C23}}, "|_") → text49
  48. TableText({{A24, B24, C24}}, "|_") → text50
  49. TableText({{E23}}, "|_") → text52
  50. TableText({{A26, B26, C26}}, "|_") → text57
  51. TableText({{A27, B27, C27}}, "|_") → text58
  52. TableText({{A28, B28, C28}}, "|_") → text59
  53. TableText({{E26}}, "|_") → text60
  54. TableText({{E27}}, "|_") → text61
  55. TableText({{E28}}, "|_") → text62
  56. Segment(B, C) → j_1
  57. IntersectPath(e, f) → s_1
  58. Segment(J, K) → f_2
  59. IntersectPath(d, c) → g_2
  60. Segment(L, M) → h_2
  61. RotateText(text63, 90°) → text64
  62. IntersectPath(h, d) → j_2
  63. TableText({{E20}}, "|_") → text65
  64. TableText({{E22}}, "|_") → text51
  65. Textfield(A2) → InputBox1
  66. Textfield(B2) → InputBox2
  67. Textfield(C2) → InputBox3
  68. Textfield(E2) → InputBox4
  69. Textfield(A3) → InputBox5
  70. Textfield(B3) → InputBox6
  71. Textfield(C3) → InputBox7
  72. Textfield(E3) → InputBox8
  73. Textfield(A4) → InputBox9
  74. Textfield(B4) → InputBox10
  75. Textfield(C4) → InputBox11
  76. Textfield(E4) → InputBox12
  77. IntersectPath(i, n) → p_2

AI Drawing Prompt Reference

Draw the intersection lines of three planes in 3D space, showing their intersections, label key points, connect these points with line segments, display plane equations and vector information, list relevant data in tables, and show coordinates in fraction and decimal forms.
The prompt above was compiled from the original drawing commands and is for reference only.