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Vector Addition Demonstration

Vector Addition Demonstration
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2020-04-14 15:20
VectorCoordinate GeometryGeometric Construction
This example demonstrates the addition of two vectors in a two-dimensional plane, visually showing the parallelogram and triangle laws of vector addition. Core math concepts include vectors, vector addition, two-dimensional space, and geometric representation. It utilizes GeoGebra commands and objects like Vector, Translate, and Midpoint to construct vectors, perform translations, and determine midpoints. Suitable for high school mathematics students learning the geometric meaning of vector addition and university-level physics courses.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(C, D) → v
  3. Translate(A, Vector[(If[a < 3, a / 3, 1] * Vector[A, E])]) → A'
  4. Translate(B, Vector[(If[a < 3, a / 3, 1] * Vector[A, E])]) → B'
  5. Vector(A', B') → w
  6. Translate(C, Vector[(If[a ≤ 3, 0, If[3 < a < 6, (a - 3) / 3, 1]] * Vector[C, B'])]) → C'
  7. Translate(D, Vector[(If[a ≤ 3, 0, If[3 < a < 6, (a - 3) / 3, 1]] * Vector[C, B'])]) → D'
  8. Vector(C', D') → b
  9. Translate(E, Vector[(If[a ≤ 6, 0, If[6 < a < 9, (a - 6) / 3, 1]] * Vector[E, D'])]) → E'
  10. Vector(E, E') → c
  11. Translate(A, Vector[(If[d < 3, d / 3, 1] * Vector[A, F])]) → A'_1
  12. Translate(B, Vector[(If[d < 3, d / 3, 1] * Vector[A, F])]) → B'_1
  13. Vector(A'_1, B'_1) → e
  14. Translate(C, Vector[(If[d ≤ 3, 0, If[3 < d < 6, (d - 3) / 3, 1]] * Vector[C, A'_1])]) → C'_1
  15. Translate(D, Vector[(If[d ≤ 3, 0, If[3 < d < 6, (d - 3) / 3, 1]] * Vector[C, A'_1])]) → D'_1
  16. Vector(C'_1, D'_1) → f
  17. Translate(B'_1, Vector[(If[d ≤ 6, 0, If[6 < d < 9, (d - 6) / 3, 1]] * Vector[C, D])]) → G
  18. Translate(D'_1, Vector[(If[d ≤ 6, 0, If[6 < d < 9, (d - 6) / 3, 1]] * Vector[A, B])]) → H
  19. Translate(C'_1, Vector[(If[d ≤ 6, 0, If[6 < d < 9, (d - 6) / 3, 1]] * Vector[C, D])]) → I
  20. Translate(A'_1, Vector[(If[d ≤ 6, 0, If[6 < d < 9, (d - 6) / 3, 1]] * Vector[A, B])]) → J
  21. Vector(J, H) → h
  22. Vector(I, G) → g
  23. Translate(F, Vector[(If[d ≤ 9, 0, If[9 < d < 12, (d - 9) / 3, 1]] * Vector[F, H])]) → K
  24. Vector(F, K) → i
  25. Midpoint(B, A) → L
  26. Midpoint(C, D) → M
  27. Midpoint(C', D') → N
  28. Midpoint(B'_1, A'_1) → P
  29. Midpoint(C'_1, D'_1) → Q
  30. Midpoint(F, K) → R
  31. Midpoint(B', A') → O
  32. Midpoint(E, E') → S

AI Drawing Prompt Reference

Draw two vectors in a 2D plane starting from different points, demonstrating the parallelogram and triangle laws of vector addition. First show the original vectors, then construct their sum via translation, animating the translation steps. Repeat with another pair of vectors, marking midpoints of all segments to aid geometric understanding. The figure should include multiple vectors, translated copies, and midpoint markers, clearly arranged to illustrate the geometric meaning of vector addition.
The prompt above was compiled from the original drawing commands and is for reference only.