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Associativity of Vector Addition in 3D

Associativity of Vector Addition in 3D
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2019-07-04 21:35
VectorSolid Geometry
This example demonstrates the associativity of vector addition in three-dimensional space, illustrating the geometric meaning of (v1 + v2) + v3 = v1 + (v2 + v3). Key math concepts include vector addition, geometric transformations, associativity, and special points. The construction leverages GeoGebra commands and objects such as Intersect, Vector, Dilate, and Translate as outlined in the summary. It is suitable for high school students and math enthusiasts to explore vector operations and spatial geometric properties, serving as an educational tool for demonstrations and inquiry-based learning.

GeoGebra Commands & Parameters

  1. Intersect(zAxis, xAxis) → A
  2. Vector(A, B) → v
  3. Vector(A, C) → u
  4. Vector(A, D) → w
  5. Dilate(A, 1 - (2 * n), B) → A'
  6. Vector(A, A') → a
  7. Translate(A, a) → A'_1
  8. Translate(C, a) → C'
  9. Vector(A'_1, C') → b
  10. Translate(C, v) → C'_1
  11. Vector(B, C'_1) → c
  12. Vector(A, C'_1) → d
  13. Dilate(A, 1 - (4 * (n - 0.5)), C'_1) → A'_2
  14. Vector(A, A'_2) → e
  15. Dilate(A, 1 - (8 * (n - 0.75)), C'_1) → A'_3
  16. Vector(A, A'_3) → f
  17. Translate(A, f) → A'_4
  18. Translate(D, f) → D'
  19. Vector(A'_4, D') → g
  20. Vector(A'_3, A'_4) → h
  21. Translate(D, d) → D'_1
  22. Vector(C'_1, D'_1) → i
  23. Dilate(A, 1 - (8.35 * (n - 0.88)), D'_1) → A'_5
  24. Vector(A, A'_5) → j
  25. Dilate(A, 1 - (2 * m), C) → A'_6
  26. Vector(A, A'_6) → k
  27. Translate(A, k) → A'_7
  28. Translate(D, k) → D'_2
  29. Vector(A'_7, D'_2) → l
  30. Translate(D, u) → D'_3
  31. Vector(C, D'_3) → p
  32. Dilate(A, 1 - (4 * (m - 0.5)), D'_3) → A'_8
  33. Vector(A, A'_8) → q
  34. Vector(A, D'_3) → r
  35. Dilate(A, 1 - (8 * (m - 0.75)), B) → A'_9
  36. Vector(A, A'_9) → s
  37. Translate(A, s) → A'_{10}
  38. Translate(D'_3, s) → E
  39. Vector(A'_{10}, E) → t
  40. Translate(D'_3, v) → F
  41. Vector(B, F) → a_1
  42. Dilate(A, 1 - (8.3 * (m - 0.88)), F) → A'_{11}
  43. Vector(A, A'_{11}) → b_1