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Vector Addition Demonstration by Barb Newitt

Vector Addition Demonstration by Barb Newitt
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2016-09-28 09:54
TriangleAngleVectorGeometric Construction
① This example demonstrates how to perform vector addition in a Cartesian plane using geometric construction, visually showing the formation of the resultant vector. ② Core mathematical concepts include the definition of vectors, component decomposition, the parallelogram law, and the geometric interpretation of vector addition. ③ Construction highlights: OrthogonalLine for perpendicular lines, Point for key points, Angle for angle marking, Vector for direct vector creation, Midpoint for midpoints, If for conditional logic, AngularBisector for angle bisectors, Circle for circles, Intersect for intersection points, Distance for length measurement; objects such as A, B, C, u, v, w, α, β, k and text labels are employed. ④ Suitable for high‑school vector lessons, introductory linear algebra demonstrations, and interactive GeoGebra courseware.

GeoGebra Commands & Parameters

  1. OrthogonalLine(C, yAxis) → g
  2. Point(g) → D
  3. OrthogonalLine(A, xAxis) → f
  4. Point(f) → B
  5. Angle(D, A, B) → β
  6. Vector(C, D) → u
  7. Vector(A, B) → v
  8. Midpoint(C, D) → E
  9. Midpoint(A, B) → F
  10. Vector(C, B) → w
  11. If(ax ≟ dx, If[ay ≟ dy, 1, 0], 0) → k
  12. Angle(D, C, B) → α
  13. AngularBisector(D, C, B) → h
  14. Circle(C, 2) → c
  15. Intersect(c, h) → G, H
  16. Midpoint(C, B) → I
  17. Distance(C, B) → distanceCB
  18. If(abs(ax - dx) < 0.1, If[abs(ay - dy) < 0.1, 1, 0], 0) → Test1
  19. Vector(A, D) → b
  20. Distance(A, D) → distanceAD
  21. If(abs(ax - cx) < 0.1, If[abs(by - dy) < 0.1, 1, 0], 0) → Test2
  22. AngularBisector(D, A, B) → i
  23. Circle(A, 2) → e
  24. Intersect(e, i) → J, K
  25. Midpoint(A, D) → L
  26. Angle(B, A, D) → γ
  27. If(abs(ax - dx) < 0.1, If[abs(ay - dy) < 0.1, 1, 0], 0) → a
  28. If(α < 90°, 1, 0) → Testa
  29. If(β < 90°, 1, 0) → Testb
  30. Angle(B, C, D) → δ
  31. If(γ < 90°, 1, 0) → Testc
  32. If(δ < 90°, 1, 0) → Testd
  33. Intersect(e, i, 2) → M
  34. Intersect(c, h, 2) → N
  35. Vector(O, P) → d
  36. Vector(O, Q) → l
  37. Vector(Q, P) → m
  38. Angle(P, O, Q) → ε
  39. Angle(Q, O, P) → ζ
  40. Distance(O, P) → distanceOP
  41. Midpoint(O, Q) → R
  42. Midpoint(Q, P) → S
  43. Midpoint(O, P) → T
  44. AngularBisector(P, O, Q) → n
  45. Circle(O, 2) → p
  46. Intersect(p, n, 2) → U
  47. If(ε < 90°, If[j < 1, 1, 0], 0) → Teste
  48. If(ζ < 90°, If[j < 1, 1, 0], 0) → Testf