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Vector Addition and Subtraction Demo

Vector Addition and Subtraction Demo
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2019-03-20 10:26
VectorCoordinate GeometryGeometric Construction
This example dynamically demonstrates vector addition and subtraction, visually illustrating vector composition and decomposition using the parallelogram and triangle rules. Core math concepts include vectors, magnitude, direction, and geometric constructions. GeoGebra commands like Dilate, Segment, Line, Vector, Intersect, Rotate, and Point are utilized to construct the demonstration, making it suitable for high school students learning vector operations or for educational purposes.

GeoGebra Commands & Parameters

  1. Dilate(D, If[0 ≤ b < 1, 1 - b, 0], H) → D''
  2. Segment(D, D'') → k
  3. Line(C, k) → l
  4. Vector(D, C) → v
  5. Line(D'', v) → m
  6. Intersect(l, m) → I
  7. Dilate(A, If[1 ≤ b < 2, 2 - b, 0], I) → A'''
  8. Line(A, A''') → p
  9. Line(B, p) → q
  10. Vector(A, B) → u
  11. Line(A''', u) → n
  12. Intersect(n, q) → J
  13. Vector(A''', J) → r
  14. Rotate(r, If[2 ≤ b ≤ 3, ((b - 2) * 180°), 180°], A''') → r'
  15. Point(r') → L
  16. Dilate(A, If[0 ≤ a < 1, 1 - a, 0], E) → A'
  17. Vector(A, A') → w
  18. Line(A', u) → f
  19. Line(B, w) → g
  20. Intersect(f, g) → F
  21. Vector(A', F) → u'
  22. Dilate(D, If[1 ≤ a < 2, 2 - a, 0], F) → D'
  23. Segment(D', D) → h
  24. Line(D', v) → i
  25. Line(C, h) → j
  26. Intersect(i, j) → G
  27. Vector(D', G) → c
  28. Dilate(A', If[2 ≤ a < 3, 3 - a, 0], G) → A''
  29. Vector(A', A'') → d
  30. Vector(D'', I) → e
  31. Dilate(D'', If[3 ≤ b ≤ 4, 4 - b, 0], L) → D'''
  32. Vector(D'', D''') → s

AI Drawing Prompt Reference

Draw a dynamic demonstration of vector addition and subtraction, visually illustrating vector composition and decomposition using the parallelogram and triangle rules. Include two vectors, constructing their sum via the parallelogram method and their difference via the triangle method. The final image should clearly show the vectors' start and end points, directions, magnitudes, and the relationships between intermediate construction points, suitable for educational purposes.
The prompt above was compiled from the original drawing commands and is for reference only.