三维向量探索

三维向量探索
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2019-04-22 11:21
这个范例演示了三维空间中的向量。核心数学概念包括向量的加减法、点乘和叉乘。通过使用GeoGebra命令如Vector、Translate、Line等,可以直观地展示向量的几何意义和运算规则。适合高中及以上学生学习三维向量的相关知识。

GeoGebra 命令及参数

  1. Vector(A) → u
  2. Vector(B) → v
  3. Vector(C) → w
  4. Textfield(k) → InputBox1
  5. Textfield(l) → InputBox2
  6. Textfield(m) → InputBox3
  7. Translate(D, c) → D'
  8. Vector(D, D') → f
  9. Translate(E, b) → E'
  10. Vector(E, E') → g
  11. Translate(E', d) → E''
  12. Vector(E', E'') → h
  13. Translate(F, e) → F'
  14. Vector(F, F') → i
  15. Textfield(x1) → InputBox4
  16. Textfield(y1) → InputBox5
  17. Textfield(z1) → InputBox6
  18. Textfield(x2) → InputBox7
  19. Textfield(y2) → InputBox8
  20. Textfield(z2) → InputBox9
  21. Textfield(x3) → InputBox10
  22. Textfield(y3) → InputBox11
  23. Line(G, v) → r
  24. OrthogonalLine(A, r, space) → s
  25. Intersect(s, r) → I
  26. Vector(I) → p
  27. Segment(A, I) → f_1
  28. OrthogonalLine(A, o) → g_1
  29. OrthogonalLine(B, o) → h_1
  30. OrthogonalLine(C, o) → i_1
  31. OrthogonalLine(C, zAxis, space) → j_1
  32. OrthogonalLine(B, zAxis, space) → k_1
  33. OrthogonalLine(A, zAxis, space) → l_1
  34. Intersect(g_1, o) → J
  35. Intersect(h_1, o) → K
  36. Intersect(i_1, o) → L
  37. Segment(A, J) → m_1
  38. Segment(B, K) → n_1
  39. Segment(C, L) → p_1
  40. Intersect(k_1, zAxis) → M
  41. Intersect(l_1, zAxis) → N
  42. Intersect(j_1, zAxis) → O
  43. Segment(A, N) → q_1
  44. Segment(B, M) → r_1
  45. Segment(C, O) → s_1
  46. OrthogonalLine(J, xAxis, space) → t_1
  47. OrthogonalLine(J, yAxis, space) → a_1
  48. OrthogonalLine(K, yAxis, space) → b_1
  49. OrthogonalLine(K, xAxis, space) → c_1
  50. OrthogonalLine(L, yAxis, space) → d_1
  51. OrthogonalLine(L, xAxis, space) → e_1
  52. Intersect(yAxis, d_1) → P
  53. Intersect(a_1, yAxis) → Q
  54. Intersect(b_1, yAxis) → R
  55. Intersect(xAxis, t_1) → S
  56. Intersect(c_1, xAxis) → T
  57. Intersect(e_1, xAxis) → U
  58. Segment(L, U) → f_2
  59. Segment(L, P) → g_2
  60. Segment(K, R) → h_2
  61. Segment(K, T) → i_2
  62. Segment(J, S) → j_2
  63. Segment(J, Q) → k_2
  64. OrthogonalLine(D, o) → l_2
  65. OrthogonalLine(E, o) → m_2
  66. OrthogonalLine(F, o) → n_2
  67. OrthogonalLine(D, zAxis, space) → p_2
  68. OrthogonalLine(E, zAxis, space) → q_2
  69. OrthogonalLine(F, zAxis, space) → r_2
  70. Intersect(p_2, zAxis) → V
  71. Intersect(q_2, zAxis) → W
  72. Intersect(r_2, zAxis) → Z
  73. Intersect(l_2, o) → A_1
  74. Intersect(m_2, o) → B_1
  75. Intersect(n_2, o) → C_1
  76. OrthogonalLine(A_1, xAxis, space) → s_2
  77. OrthogonalLine(B_1, xAxis, space) → t_2
  78. OrthogonalLine(C_1, xAxis, space) → a_2
  79. OrthogonalLine(A_1, yAxis, space) → b_2
  80. OrthogonalLine(B_1, yAxis, space) → c_2
  81. OrthogonalLine(C_1, yAxis, space) → d_2
  82. Intersect(s_2, xAxis) → D_1
  83. Intersect(t_2, xAxis) → E_1
  84. Intersect(a_2, xAxis) → F_1
  85. Intersect(b_2, yAxis) → G_1
  86. Intersect(c_2, yAxis) → H_1
  87. Intersect(d_2, yAxis) → I_1
  88. Segment(D, V) → e_2
  89. Segment(D, A_1) → f_3
  90. Segment(A_1, D_1) → g_3
  91. Segment(A_1, G_1) → h_3
  92. Segment(E, W) → i_3
  93. Segment(E, B_1) → j_3
  94. Segment(B_1, H_1) → k_3
  95. Segment(B_1, E_1) → l_3
  96. Segment(F, Z) → m_3
  97. Segment(F, C_1) → n_3
  98. Segment(C_1, I_1) → p_3
  99. Segment(C_1, F_1) → q_3
  100. Textfield(z3) → InputBox12

AI 绘图提示语参考

绘制三维空间中的向量及其运算。首先创建三个向量u、v、w,然后通过平移和向量运算生成新的向量f、g、h、i。接着输入x1、y1、z1等坐标值,构造点和线,利用点和线的交点生成新的向量和线段,最终展示向量的加减法、点积和叉积。
以上提示语为根据原始绘图命令整理而来,仅供参考。