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平面方程的解与交线演示

平面方程的解与交线演示
几何画板及绘图内容加载中，请稍等……
2017-09-15 09:52
向量函数解析几何立体几何
①本范例演示了三个平面在三维空间中的交线情况；②涉及的核心数学概念包括平面方程、三维解析几何、向量积与线性组合；③作图要点提炼自构造摘要，使用了IntersectPath（交点计算）、FractionText（分数文本显示）、TableText（表格文本）、Segment（线段绘制）、RotateText（文本旋转）、Textfield（文本字段）等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于理解立体几何与线性代数中的平面交线问题。

GeoGebra 命令及参数

  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 绘图提示语参考

在三维空间中绘制三个平面的交线，展示它们的相交情况，并标注关键点，用线段连接这些交点，同时显示平面方程和向量信息，用表格列出相关数据，并用分数和小数形式展示坐标值。
以上提示语为根据原始绘图命令整理而来，仅供参考。