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Equal Vectors Recognition Exercises (03)

Equal Vectors Recognition Exercises (03)
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2014-01-07 12:14
PolygonVectorTransformationGeometric Construction
In collections Complex Numbers as Vectors
This interactive applet provides a set of exercises focused on recognizing equal vectors in geometric configurations. It demonstrates that two vectors are equal if they have the same magnitude and direction, regardless of their starting point. The core mathematical concept is the definition of vector equality and the idea of translation invariance. The construction uses GeoGebra commands such as Polygon, Segment, Intersect, Vector, and Translate to build polygons, segments, intersection points, vectors, and translated copies. Text objects (text1, text2, text3) are included to present prompts or feedback. This resource is suitable for high school or introductory college students learning vector basics, and can be used for self-study or classroom demonstration. By comparing vectors placed at different positions, learners gain an intuitive understanding of why equal vectors are not tied to a specific location.

GeoGebra Commands & Parameters

  1. Polygon(A, B, 6) → poly1, a, F, b, c, d, e, f, C, D, E
  2. Segment(F, A) → g
  3. Segment(A, B) → h
  4. Segment(B, C) → i
  5. Segment(C, D) → j
  6. Segment(D, E) → k
  7. Segment(E, F) → l
  8. Segment(E, B) → m
  9. Segment(D, A) → n
  10. Segment(F, C) → p
  11. Intersect(m, n) → H
  12. Vector(F, E) → u
  13. Translate(G, u) → G'
  14. Translate(I, u) → I'
  15. Translate(J, u) → J'
  16. Translate(K, u) → K'
  17. Vector(C, H) → r
  18. Translate(L, r) → L'
  19. Translate(M, r) → M'
  20. Translate(N, r) → N'
  21. Translate(O, r) → O'
  22. Vector(E, H) → w_1
  23. Translate(P, w_1) → P'
  24. Translate(Q, w_1) → Q'
  25. Translate(R, w_1) → R'
  26. Translate(S, w_1) → S'
  27. Polygon(A_1, B_1, 6) → poly1_1, a_3, F_1, b_3, c_3, d_1, e_1, f_1, C_1, D_1, E_1
  28. Segment(F_1, A_1) → g_1
  29. Segment(A_1, B_1) → h_1
  30. Segment(B_1, C_1) → i_1
  31. Segment(C_1, D_1) → j_1
  32. Segment(D_1, E_1) → k_1
  33. Segment(E_1, F_1) → l_1
  34. Segment(E_1, B_1) → m_1
  35. Segment(D_1, A_1) → n_1
  36. Segment(F_1, C_1) → p_1
  37. Intersect(m_1, n_1) → H_1
  38. Vector(F_1, E_1) → u_3
  39. Translate(G_1, u_3) → G'_1
  40. Vector(G_1, G'_1) → v_2
  41. Translate(I_1, u_3) → I'_1
  42. Vector(I_1, I'_1) → w_2
  43. Translate(J_1, u_3) → J'_1
  44. Vector(J_1, J'_1) → z_2
  45. Translate(K_1, u_3) → K'_1
  46. Vector(K_1, K'_1) → q_1
  47. Vector(C_1, H_1) → r_1
  48. Translate(L_1, r_1) → L'_1
  49. Vector(L_1, L'_1) → s_1
  50. Translate(M_1, r_1) → M'_1
  51. Vector(M_1, M'_1) → t_1
  52. Translate(N_1, r_1) → N'_1
  53. Vector(N_1, N'_1) → u_2
  54. Translate(O_1, r_1) → O'_1
  55. Vector(O_1, O'_1) → v_3
  56. Vector(E_1, H_1) → w_3
  57. Translate(P_1, w_3) → P'_1
  58. Vector(P_1, P'_1) → z_3
  59. Translate(Q_1, w_3) → Q'_1
  60. Vector(Q_1, Q'_1) → a_2
  61. Translate(R_1, w_3) → R'_1
  62. Vector(R_1, R'_1) → b_2
  63. Translate(S_1, w_3) → S'_1
  64. Vector(S_1, S'_1) → c_2

AI Drawing Prompt Reference

Draw a hexagon ABCDEF, connect F to A, A to B, B to C, C to D, D to E, and E to F, then connect E to C, D to A, and F to C to find their intersection point H. Draw vector FE, then translate G, I, J, and K along vector FE to get G', I', J', and K'. Next, draw vector CH, then translate L, M, N, and O along vector CH to get L', M', N', and O'. Finally, draw vector EH, then translate P, Q, R, and S along vector EH to get P', Q', R', and S'.
The prompt above was compiled from the original drawing commands and is for reference only.