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3D Vectors and Symmetry in Equilateral Triangles

3D Vectors and Symmetry in Equilateral Triangles
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2018-12-23 03:53
VectorTrigonometrySolid GeometryGeometric Construction
This example demonstrates the relationship between 3D vectors, equilateral triangles, and symmetry in three-dimensional space using GeoGebra. It involves core mathematical concepts such as 3D vectors, equilateral triangle construction, symmetry analysis, and trigonometric applications. The construction utilizes commands and objects like Point, Element, Intersect, Circle, Segment, Angle, OrthogonalLine, CircleArc, and Vector for precise geometric modeling and dynamic visualization. Suitable for high school and advanced learners to understand spatial geometry, vector operations, and symmetry principles.

GeoGebra Commands & Parameters

  1. Point(yAxis) → E
  2. Element(fnl, function) → g
  3. Intersect(xAxis, yAxis) → A
  4. Circle(A, B) → c
  5. Segment(A, C) → a
  6. Segment(B, A) → b
  7. Angle(B, A, C) → α
  8. OrthogonalLine(C, yAxis) → d
  9. Intersect(d, yAxis) → D
  10. CircleArc(A, B, C) → e
  11. Vector(C, D) → u
  12. Vector(E, F) → v
  13. Segment(D, A) → h
  14. Segment(H, B) → i
  15. Vector(t, C) → w
  16. OrthogonalLine(C, b) → j
  17. Intersect(j, i) → I
  18. Vector(C, I) → z
  19. Vector(I, J) → k
  20. Vector(E, K) → l
  21. Vector(L, K) → n
  22. Segment(S, U) → b_1
  23. Segment(P, Q) → c_1
  24. Segment(R, T) → a_1
  25. Vector(M, V) → p
  26. Vector(C_1, W) → v_1
  27. Segment(V, A) → g_1
  28. Vector(L, A_1) → m
  29. Element(fnnl, function) → fnn
  30. Vector(C_1, W) → u_1
  31. Vector(V, Z) → z_1
  32. Vector(C, W) → h_1
  33. Vector(V, Z) → j_1
  34. Segment(A, V) → k_1
  35. CircleArc(A, V, H) → p_1
  36. Segment((0, π), L) → r
  37. Segment((-1.5, π), M) → q
  38. Vector(V, (x(V), 0)) → w_1
  39. Vector(E_1, C_1) → z_2
  40. Vector(I, F_1) → l_1
  41. Vector(F_1, G_1) → m_1
  42. Vector(C, G_1) → i_1