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3D Vector Visualization

3D Vector Visualization
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2013-01-09 06:02
VectorSolid GeometryGeometric Construction
In collections C4 vectors
This example demonstrates the visualization of 3D vectors, covering core mathematical concepts like vector addition, reflection, and orthogonal lines. It utilizes commands such as Vector, OrthogonalLine, Translate, Midpoint, Line, Mirror, Segment, Intersect, and Polygon in GeoGebra for construction. Suitable for high school and above students learning 3D vectors and operations.

GeoGebra Commands & Parameters

  1. Vector(B_1, X) → p
  2. Vector(B_1, Z) → w
  3. OrthogonalLine(View3d, yAxis) → a
  4. OrthogonalLine(View3d, xAxis) → b
  5. Vector(B_1, Y) → v
  6. Translate(O, Vector[xM * p]) → A
  7. Translate(A, Vector[yM * v]) → B
  8. Translate(B, Vector[zM * w]) → M
  9. Vector(O, M) → z
  10. Midpoint(O, M) → C1
  11. Translate(O, w) → G
  12. Line(O, G) → e
  13. Translate(O, Vector[5 * w]) → H
  14. Translate(O, Vector[-6 * w]) → I
  15. Vector(I, H) → h
  16. Translate(O, p) → K
  17. Translate(O, Vector[6 * p]) → L
  18. Mirror(L, O) → M_1
  19. Vector(M_1, L) → j
  20. Translate(O, v) → N
  21. Translate(O, Vector[6 * v]) → P
  22. Mirror(P, O) → Q
  23. Segment(A, B) → d
  24. Line(B, j) → n
  25. Segment(M, B) → q
  26. Translate(O, Vector[zM * w]) → E
  27. Segment(E, M) → r
  28. Vector(Q, P) → l
  29. Line(B, j) → f
  30. Segment(Q, P) → i
  31. Vector(O, G) → p_1
  32. Vector(O, K) → s
  33. Vector(O, N) → t
  34. Midpoint(O, K) → F
  35. Midpoint(O, N) → J
  36. Midpoint(G, O) → R
  37. Mirror(O, K) → D
  38. Mirror(K, D) → S
  39. Mirror(D, S) → T
  40. Mirror(S, T) → U
  41. Mirror(K, O) → V
  42. Mirror(O, V) → W
  43. Mirror(V, W) → A1
  44. Mirror(W, A1) → B1
  45. Mirror(A1, B1) → D1
  46. Mirror(O, N) → E1
  47. Mirror(N, E1) → F1
  48. Mirror(E1, F1) → G1
  49. Mirror(G1, F1) → H1
  50. Mirror(F1, G1) → I1
  51. Mirror(N, O) → J1
  52. Mirror(O, J1) → K1
  53. Mirror(J1, K1) → L1
  54. Mirror(K1, L1) → M1
  55. Mirror(L1, M1) → N1
  56. Mirror(O, G) → O1
  57. Mirror(G, O1) → P1
  58. Mirror(O1, P1) → Q1
  59. Mirror(G, O) → R1
  60. Mirror(O, R1) → S1
  61. Mirror(R1, S1) → U1
  62. Mirror(S1, U1) → V1
  63. Mirror(U1, V1) → W1
  64. Translate(N, s) → Z1
  65. Line(L, l) → m
  66. Line(P, j) → a1
  67. Line(M_1, l) → b1
  68. Line(Q, j) → c1
  69. Intersect(b1, c1) → A2
  70. Intersect(m, c1) → B2
  71. Intersect(a1, m) → C2
  72. Intersect(a1, b1) → D2
  73. Polygon(A2, B2, C2, D2) → poly1, a2, b2, c2, d2
  74. Line(H, j) → d1
  75. Line(L, h) → e1
  76. Line(M_1, h) → f1
  77. Line(I, d1) → g1
  78. Intersect(d1, f1) → E2
  79. Intersect(e1, d1) → F2
  80. Intersect(g1, e1) → G2
  81. Intersect(g1, f1) → H2
  82. Polygon(E2, F2, G2, H2) → poly2, e2, f2, g2, h2
  83. Line(H, l) → h1
  84. Line(Q, h) → i1
  85. Line(P, h) → j1
  86. Line(I, l) → k1
  87. Intersect(h1, i1) → I2
  88. Intersect(j1, h1) → J2
  89. Intersect(k1, j1) → K2
  90. Intersect(i1, k1) → L2
  91. Polygon(I2, J2, K2, L2) → poly3, i2, j2, k2, l2
  92. Line(B, j) → l1
  93. Segment(O, P) → m1
  94. Intersect(l1, m1) → M2
  95. Segment(M2, B) → n1
  96. Segment(O, M2) → b_1
  97. Segment(O, A) → a_1
  98. Segment(A, C) → c_1
  99. Segment(C, M) → d_1
  100. Segment(M, A_1) → e_1
  101. Segment(O, E) → f_1
  102. Segment(C, E) → g_1
  103. Segment(E, A_1) → h_1
  104. Segment(A_1, M2) → i_1
  105. Segment(A, C) → j_1

AI Drawing Prompt Reference

Create a 3D vector visualization, including vectors p, w, and v, and their linear combinations forming point M, as well as the mirror image of vector w through the origin O. Start by drawing vectors p and w, then draw vector v, and construct point M using vectors p and w. Next, draw line e through origin O and vector w, then construct the mirror image of vector w, and finally draw vectors p, v, and their linear combinations forming point M, and connect related points to form segments and lines.
The prompt above was compiled from the original drawing commands and is for reference only.