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3D Vectors and Coordinate Geometry Interactive Demo

3D Vectors and Coordinate Geometry Interactive Demo
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2022-04-09 10:19
VectorCoordinate GeometrySolid GeometryGeometric Construction
In collections Gamified Math Exercises
This example demonstrates 3D vector operations and coordinate geometry problems interactively in space; involves core concepts like 3D vectors, coordinates, point-line-plane relationships, geometric constructions; constructed using GeoGebra commands/objects such as RandomElement, Ray, OrthogonalLine, Circle, Line, Polygon; suitable for high school and above students to understand solid geometry and vector knowledge, or for mathematical teaching demonstrations.

GeoGebra Commands & Parameters

  1. RandomElement(l2) → b, 5
  2. RandomElement(l1) → a, 5
  3. Textfield(P) → InputBox1
  4. Intersect(xAxis, yAxis) → A
  5. Ray(A, P) → f
  6. OrthogonalLine(A, f) → g
  7. Circle(A, 0.3) → c
  8. Intersect(c, g, 1) → B
  9. Intersect(c, g, 2) → C
  10. Circle(A, 0.4) → d
  11. Intersect(d, g, 1) → D
  12. Intersect(d, g, 2) → E
  13. OrthogonalLine(E, g) → h
  14. OrthogonalLine(C, g) → i
  15. OrthogonalLine(D, g) → j
  16. OrthogonalLine(B, g) → k
  17. Intersect(d, k, 2) → F
  18. Intersect(d, i, 2) → G
  19. OrthogonalLine(F, k) → m
  20. Intersect(d, k, 1) → H
  21. OrthogonalLine(H, k) → n
  22. Intersect(h, m) → I
  23. Intersect(h, n) → J
  24. Intersect(j, n) → K
  25. Circle(A, 0.1) → e
  26. Intersect(e, g, 1) → L
  27. Intersect(e, g, 2) → M
  28. Line(L, f) → p
  29. Line(M, f) → q
  30. Intersect(i, n) → O
  31. Intersect(j, m) → Q
  32. Circle(D, 0.03) → r
  33. Intersect(d, r, 1) → R
  34. Mirror(R, g) → R'
  35. OrthogonalLine(D, j) → s
  36. OrthogonalLine(R', j) → t
  37. OrthogonalLine(R, j) → f_1
  38. Intersect(t, h) → S
  39. Intersect(f_1, h) → U
  40. Polygon(R', R, U, S) → q1, r', r_1, u, s_1
  41. Polygon(Q, K, H, F) → q2, q_1, k_1, h_1, f_2
  42. Polygon(G, O, J, I) → q3, g_1, o, j_1, i_1
  43. Circle(A, 0.8) → c_1
  44. Intersect(m, p) → W
  45. Intersect(m, q) → Z
  46. Midpoint(W, L) → A_1
  47. Midpoint(Z, M) → B_1
  48. Midpoint(A_1, B_1) → C_1
  49. Polygon(A_1, L, M, B_1) → q5, a_1, l_2, m_3, b_1
  50. Circle(C_1, B_1) → p_1
  51. Circle(A, v) → t_1
  52. Intersect(t_1, f, 1) → H_1
  53. Polygon(R_1, K_1, D_2, V_1, U_1, M_1, N_1, O_1, P_1, F_2, E_2, Q_1, L_1, T_1, S_1, A_2, B_2, W_1, Z_1, C_2) → poly1, l, c_2, d_2, v_1, u_1, k_2, n_2, o_1, p_2, q_2, e_2, g_2, r_2, h_2, i_2, j_2, a_2, b_2, w_1, z_1
  54. Midpoint(W_1, Z_1) → G_2
  55. Circle(G_2, Z_1) → s_2
  56. Defined(P) → w
  57. Intersect(c_1, f, 1) → I_2
  58. Circle(I_2, 0.05) → t_2
  59. Intersect(c_1, t_2, 1) → J_2
  60. Intersect(c_1, t_2, 2) → K_2
  61. Intersect(p, f_1) → L_2
  62. Intersect(q, f_1) → M_2
  63. Intersect(q, t) → N
  64. Intersect(t, p) → V
  65. Polygon(N, J_2, K_2, V) → q4, n_1, l_1, m_1, v_2
  66. Polygon(M, K_2, J_2, L) → q6, m_2, d_1, e_1, l_3
  67. Distance(A, P) → o_2
  68. If(Defined[Distance[A, P]], Distance[A, P], 1) → maxslider

AI Drawing Prompt Reference

Create an interactive 3D demonstration showing vector operations and coordinate geometry. Start from a random point, draw rays intersecting coordinate axes, and construct perpendicular lines, circles, and polygons. Use these geometric objects to illustrate relationships between points, lines, and planes, and display the geometric construction process, suitable for high school and above students to understand solid geometry and vectors.
The prompt above was compiled from the original drawing commands and is for reference only.