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空间直线

空间直线
几何画板及绘图内容加载中，请稍等……
2019-02-18 03:21
向量解析几何立体几何
这个范例演示了空间中的直线。涉及的核心数学概念包括三维向量和直线方程。通过使用GeoGebra命令如`Vector`、`Line`和`Intersect`等，可以构造出空间直线。适合高中数学教学和学习三维几何的学生。

GeoGebra 命令及参数

  1. If(f ∧ i_1 ≟ true, v_1, x(A)) → b
  2. Vector((0, 0, 0), C) → v
  3. Vector(A, B) → u
  4. If(f ∧ i_1 ≟ true, a_2, z(A)) → d
  5. If(f ∧ (b_1 ∨ i_1) ≟ true, a_2, d) → s_1
  6. If(f ∧ i_1 ≟ true, w_1, y(A)) → c
  7. If(f ∧ (b_1 ∨ i_1) ≟ true, w_1, c) → p_1
  8. If(f ∧ (i_1 ∨ b_1) ≟ true, n_1, If[o ≟ true, z(u), z(v)]) → h
  9. If(f ∧ (b_1 ∨ i_1) ≟ true, v_1, b) → o_1
  10. If(f ∧ (i_1 ∨ b_1) ≟ true, l_1, If[o ≟ true, x(u), x(v)]) → e
  11. If(f ∧ b_1 ≟ true, r_1, r) → h_1
  12. If(f ∧ b_1 ≟ true, f_1, p) → g_1
  13. If(f ∧ b_1 ≟ true, q_1, q) → e_1
  14. If(f ∧ (i_1 ∨ b_1) ≟ true, m_1, If[o ≟ true, y(u), y(v)]) → g
  15. Textfield(A) → puntoA
  16. Textfield(C) → vectordir
  17. Textfield(B) → puntoB
  18. Expand((g_1(x) * h) - (e * h_1(x, y, z))) → k
  19. Expand((g_1(x) * g) - (e_1(x, y) * e)) → j
  20. Expand((e_1(x, y) * h) - (g * h_1(x, y, z))) → i
  21. If(j ≟ j_1, {k, i}, If[k ≟ k_1, {j, i}, {j, k}]) → l4
  22. Element(l4, 1) → l
  23. Element(l4, 2) → n
  24. Line((x(A), y(A), z(A)), Vector[(x(If[o ≟ true, u, v]), y(If[o ≟ true, u, v]), z(If[o ≟ true, u, v]))]) → t
  25. Textfield(A) → CasillaDeEntrada1
  26. Textfield(C) → CasillaDeEntrada2
  27. Textfield(f_1) → CasillaDeEntrada3
  28. Textfield(q_1) → CasillaDeEntrada4
  29. Textfield(r_1) → CasillaDeEntrada5
  30. Textfield(l_1) → CasillaDeEntrada6
  31. Textfield(m_1) → CasillaDeEntrada7
  32. Textfield(n_1) → CasillaDeEntrada8
  33. Expand(x - f_1(x)) → t_1
  34. Expand(y - q_1(x, y)) → d_1
  35. Expand(z - r_1(x, y, z)) → u_1
  36. Textfield(v_1) → C9
  37. Textfield(l_1) → CasillaDeEntrada10
  38. Textfield(w_1) → CasillaDeEntrada9
  39. Textfield(m_1) → CasillaDeEntrada11
  40. Textfield(a_2) → CasillaDeEntrada12
  41. Textfield(n_1) → CasillaDeEntrada13
  42. Expand(x) → d_2
  43. Expand(z) → e_2
  44. IntersectPath(k_2, l_2) → m_2
  45. OrthogonalVector(k_2) → u_2
  46. OrthogonalVector(l_2) → v_2
  47. Textfield(k_2) → CasillaDeEntrada14
  48. Textfield(l_2) → CasillaDeEntrada15
  49. Expand(x - p_2) → s_2
  50. Expand(y - q_2) → t_2
  51. Expand(z - r_2) → f_3
  52. Intersect(f_2, i_2) → I
  53. Vector(C) → u_3
  54. Vector(K) → v_3
  55. Line((x(A), y(A), z(A)), Vector[(x(u_3), y(u_3), z(u_3))]) → j_3
  56. Line((x(J), y(J), z(J)), Vector[(x(v_3), y(v_3), z(v_3))]) → k_3
  57. Determinant(m1) → l_3
  58. If(j_3 ≟ k_3, "Coincidentes", If[(x(u_3) * y(v_3)) ≟ (y(u_3) * x(v_3)) ∧ (y(u_3) * z(v_3)) ≟ (z(u_3) * y(v_3)), "Paralelas", If[l_3 ≟ 0, "Secantes", "Se\; cruzan"]]) → texto20
  59. Textfield(A) → CasillaDeEntrada16
  60. Textfield(C) → CasillaDeEntrada17
  61. Textfield(J) → CasillaDeEntrada18
  62. Textfield(K) → CasillaDeEntrada19
  63. If(j_3 ≟ k_3, 0, Distance[j_3, k_3]) → m_3
  64. Textfield(n_3) → Ca20
  65. Textfield(q_3) → CasillaDeEntrada21
  66. Textfield(o_3) → CasillaDeEntrada20
  67. Textfield(r_3) → CasillaDeEntrada22
  68. Textfield(p_3) → CasillaDeEntrada23
  69. Textfield(s_3) → CasillaDeEntrada24
  70. Textfield(t_3) → CasillaDeEntrada25
  71. Textfield(b_4) → CasillaDeEntrada26
  72. Textfield(w_3) → CasillaDeEntrada27
  73. Textfield(c_4) → CasillaDeEntrada28
  74. Textfield(a_4) → CasillaDeEntrada29
  75. Textfield(d_4) → CasillaDeEntrada30
  76. Textfield(f_4) → CasillaDeEntrada31
  77. Textfield(g_4) → CasillaDeEntrada32
  78. Textfield(i_4) → CasillaDeEntrada33
  79. Textfield(k_4) → CasillaDeEntrada34
  80. Textfield(l_4) → CasillaDeEntrada35
  81. Textfield(m_4) → CasillaDeEntrada36
  82. Textfield(p_4) → CasillaDeEntrada37
  83. Textfield(o_4) → CasillaDeEntrada38
  84. Textfield(r_4) → CasillaDeEntrada39
  85. Textfield(t_4) → CasillaDeEntrada40
  86. Textfield(u_4) → CasillaDeEntrada41
  87. Textfield(v_4) → CasillaDeEntrada42
  88. Textfield(w_4) → CasillaDeEntrada43
  89. Textfield(a_5) → CasillaDeEntrada44
  90. IntersectPath(w_4, a_5) → f_5
  91. Intersect(f_5, g_2) → M
  92. Intersect(f_5, h_2) → N
  93. Intersect(f_5, i_2) → O
  94. Element(RemoveUndefined[{M, N, O}], 1) → P
  95. IntersectPath(b_5, c_5) → g_5
  96. Intersect(g_5, g_2) → Q
  97. Intersect(g_5, h_2) → R
  98. Intersect(g_5, i_2) → S
  99. Element(RemoveUndefined[{Q, R, S}], 1) → T
  100. Textfield(b_5) → CasillaDeEntrada45
  101. Textfield(c_5) → CasillaDeEntrada46