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Vector Operations by Marsal F

Vector Operations by Marsal F
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2015-11-22 04:24
VectorCoordinate GeometryGeometric Construction
This example demonstrates basic vector operations in 2D, including addition, subtraction, and dot product; involves core concepts like vectors, Pythagorean theorem, similar triangles, polygons, and special points; constructed using commands/objects like Segment, Circle, Point, Vector, Line, Intersect, OrthogonalLine, Ray, Angle in GeoGebra; suitable for high school mathematics teaching or student exploration of vector properties.

GeoGebra Commands & Parameters

  1. Segment(A, B) → b
  2. Circle(A, B) → c_2
  3. Point(c_2) → C
  4. Segment(A, C) → d
  5. Circle(A_1, B_1) → c_1
  6. Point(c_1) → C_1
  7. Vector(A_1, C_1) → u
  8. Vector(A_1, B_1) → v
  9. Line(C_1, v) → e
  10. Line(B_1, u) → f
  11. Intersect(e, f) → D
  12. Vector(C_1, D) → w
  13. Vector(D, B_1) → g
  14. Vector(A, B) → j
  15. Line(C, j) → l
  16. Vector(A, E) → m
  17. Line(E, j) → n
  18. Line(B, m) → p
  19. Intersect(n, p) → F
  20. Segment(E, F) → q
  21. Segment(B, F) → r
  22. Vector(A, F) → s
  23. Vector(G, H) → t
  24. Vector(I, J) → u_1
  25. Line(H, u_1) → a_1
  26. Segment(I, H) → b_1
  27. Line(J, b_1) → d_1
  28. Intersect(a_1, d_1) → K
  29. Segment(H, K) → e_1
  30. Segment(J, K) → f_1
  31. Vector(G, K) → v_1
  32. Vector(A, B) → a
  33. Line(A, B) → h
  34. Circle(B, A) → k
  35. Intersect(k, h, 2) → L
  36. Circle(L, B) → g_1
  37. Intersect(g_1, h, 2) → M
  38. Vector(B, M) → i
  39. Vector(N, O) → V_1
  40. Vector(P, Q) → V_2
  41. Vector(R, S) → w_1
  42. Vector(R, T) → h_1
  43. OrthogonalLine(R, xAxis) → i_1
  44. OrthogonalLine(R, i_1) → j_1
  45. Ray(R, U) → k_1
  46. Point(i_1) → V
  47. Vector(R, V) → l_1
  48. Angle(w_1, h_1) → θ
  49. Line(T, j_1) → m_1
  50. Line(T, k_1) → n_1
  51. Line(S, j_1) → p_1
  52. Line(S, k_1) → q_1
  53. Intersect(m_1, k_1) → W
  54. Intersect(p_1, k_1) → Z
  55. Intersect(j_1, q_1) → D_1
  56. Intersect(j_1, n_1) → E_1
  57. Ray(R, D_1) → r_1
  58. Segment(S, Z) → s_1
  59. Segment(T, W) → t_1
  60. Segment(T, E_1) → a_2
  61. Segment(S, D_1) → b_2
  62. Ray(R, V) → d_2