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3D Vector Addition and Transformation Animation

3D Vector Addition and Transformation Animation
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2017-02-17 03:31
VectorSolid GeometryGeometric Construction
In collections Congruence (CO) Cluster Congruence (Vol 2) CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 CCSS High School: Geometry (Congruence) Volume 2 Gail LeBlancCCSS High School: Geometry (Congruence) Volume 2
This example demonstrates vector addition and dynamic transformations in three-dimensional space. Key math concepts include 3D vectors, addition, rotation, scaling, etc. GeoGebra commands and objects used in construction are Ray, Rotate, Vector, Translate, Dilate, etc. Suitable for high school and above students studying solid geometry and vector operations, or university-level physics teaching.

GeoGebra Commands & Parameters

  1. Ray(A, B) → f
  2. Rotate(B, (o * π / 180), A) → B'
  3. Angle(B, A, B') → β
  4. Ray(A, B') → g
  5. Point(g) → C
  6. Circle(A, C) → c
  7. Intersect(c, f, 1) → D
  8. Rotate(D, If[0 < a ≤ 1, ((a * 2) * π), (2 * π)], A) → D'
  9. Rotate(C, If[0 < a ≤ 1, (((-a) * 2) * π), (-2 * π)], A) → C'
  10. CircleArc(A, C', C) → d
  11. Ray(E, F) → h
  12. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], E) → A'
  13. Vector(A, A') → u
  14. Translate(c, u) → c'
  15. Translate(A, u) → A'_1
  16. Intersect(c', h, 1) → G
  17. Circle(C, D) → e
  18. Rotate(D, If[2 < a ≤ 3, (((-(a - 2)) * 2) * π), (-2 * π)], C) → C'_1
  19. CircleArc(C, C'_1, D) → k
  20. Dilate(C, If[3 < a ≤ 4, 4 - a, 0], G) → C'_2
  21. Vector(C, C'_2) → v
  22. Translate(e, v) → e'
  23. Translate(C, v) → C'_3
  24. Intersect(e', c') → H, I, ,
  25. Dilate(E, If[5 < a ≤ 6, 6 - a, 0], I) → E'
  26. Vector(E, E') → w
  27. Segment(E, E') → i
  28. Ray(E, I) → j
  29. Circle(I, 5) → p
  30. Intersect(p, j, 2) → J
  31. Distance(A, C) → b
  32. Circle(A, (0.5 * b)) → q
  33. Intersect(q, f, 1) → K
  34. Rotate(K, If[6.5 < a ≤ 7.5, (((a - 6.5) * o) * π / 180), (o * π / 180)], A) → K'
  35. CircleSector(A, K, K') → r
  36. Dilate(A, If[8 < a ≤ 9, 9 - a, 0], E) → A'_2
  37. Vector(A, A'_2) → m
  38. Translate(r, m) → r'
  39. Line(E, f) → n
  40. Line(E, g) → s
  41. Point(s) → L
  42. Point(n) → M
  43. Angle(L, E, I) → γ
  44. Rotate(r', If[9 < a ≤ 10, ((a - 9) * γ), γ], E) → r''
  45. Ray(E, I) → l
  46. Intersect(p, l, 2) → N
  47. Ray(I, N) → t