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3D Vector Exploration

3D Vector Exploration
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2019-04-22 11:21
VectorCoordinate GeometrySolid Geometry
This example demonstrates vectors in three-dimensional space. Key mathematical concepts include vector addition, subtraction, dot product, and cross product. Using GeoGebra commands such as Vector, Translate, and Line, the geometric meaning and operations of vectors are visually illustrated. Suitable for high school and above students to learn about 3D vectors.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw vectors in 3D space and their operations. Start by creating three vectors u, v, and w, then generate new vectors f, g, h, and i through translation and vector operations. Input coordinates x1, y1, z1, etc., to construct points and lines, and use their intersections to generate new vectors and segments, ultimately showing vector addition, subtraction, dot product, and cross product.
The prompt above was compiled from the original drawing commands and is for reference only.