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向量缩放演示

向量缩放演示
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2016-07-15 11:00
向量几何作图
所属专题 Vector Operations Vector Operations
①本范例动态演示向量与标量相乘的含义；②涉及核心数学概念：向量、标量乘法、向量长度变化；③作图要点：使用Vector、Line、Length、Circle、Intersect、Dilate、Mirror、Translate等GeoGebra命令绘制并变换向量；④适合高中数学学生理解向量运算及几何意义。

GeoGebra 命令及参数

  1. Vector(A, B) → u
  2. Line(C, u) → f
  3. Length(u) → b
  4. Circle(C, b) → c
  5. Intersect(c, f, 2) → D
  6. Circle(D, b) → d
  7. Intersect(d, f, 2) → E
  8. Circle(E, b) → e
  9. Intersect(e, f, 2) → F
  10. Circle(F, b) → g
  11. Intersect(g, f, 2) → G
  12. Circle(G, b) → h
  13. Intersect(h, f, 2) → H
  14. Circle(H, b) → k_2
  15. Intersect(k_2, f, 2) → I
  16. Circle(I, b) → p
  17. Intersect(p, f, 2) → J
  18. Circle(J, b) → q
  19. Intersect(q, f, 2) → K
  20. Circle(K, b) → r
  21. Intersect(c, f, 1) → L
  22. Circle(L, b) → s
  23. Intersect(s, f, 1) → M
  24. Circle(M, b) → t
  25. Intersect(t, f, 1) → N
  26. Circle(N, b) → c_1
  27. Intersect(c_1, f, 1) → O
  28. Circle(O, b) → d_1
  29. Intersect(d_1, f) → P, Q
  30. Circle(P, b) → e_1
  31. Intersect(e_1, f, 1) → R
  32. Circle(R, b) → f_1
  33. Intersect(f_1, f, 1) → S
  34. Circle(S, b) → g_1
  35. Intersect(g_1, f, 1) → T
  36. Circle(T, b) → h_1
  37. Intersect(h_1, f, 1) → U
  38. Dilate(C, If[0 < i ≤ 1, 1 - i, 0], D) → C'
  39. Dilate(D, If[0 < i ≤ 1, 1 - i, 0], E) → D'
  40. Dilate(E, If[0 < i ≤ 1, 1 - i, 0], F) → E'
  41. Dilate(F, If[0 < i ≤ 1, 1 - i, 0], G) → F'
  42. Dilate(G, If[0 < i ≤ 1, 1 - i, 0], H) → G'
  43. Dilate(H, If[0 < i ≤ 1, 1 - i, 0], I) → H'
  44. Dilate(I, If[0 < i ≤ 1, 1 - i, 0], J) → I'
  45. Dilate(J, If[0 < i ≤ 1, 1 - i, 0], K) → J'
  46. Mirror(C', C) → C''
  47. Mirror(D', C) → D''
  48. Mirror(E', C) → E''
  49. Mirror(F', C) → F''
  50. Mirror(G', C) → G''
  51. Mirror(H', C) → H''
  52. Mirror(I', C) → I''
  53. Mirror(J', C) → J''
  54. Vector(C, C') → v
  55. Vector(D, D') → w
  56. Vector(E, E') → j
  57. Vector(F, F') → l
  58. Vector(G, G') → m
  59. Vector(H, H') → n
  60. Vector(I, I') → u_1
  61. Vector(J, J') → v_1
  62. Vector(C, C'') → w_1
  63. Vector(L, D'') → a_1
  64. Vector(M, E'') → b_1
  65. Vector(Q, F'') → i_1
  66. Vector(O, G'') → j_1
  67. Vector(P, H'') → k_1
  68. Vector(R, I'') → l_1
  69. Vector(S, J'') → m_1
  70. Vector(C, V) → n_1
  71. Translate(E, n_1) → E'_1
  72. Translate(F, n_1) → F'_1
  73. Translate(G, n_1) → G'_1
  74. Translate(H, n_1) → H'_1
  75. Translate(I, n_1) → I'_1
  76. Translate(J, n_1) → J'_1
  77. Translate(K, n_1) → K'
  78. Translate(L, n_1) → L'
  79. Translate(M, n_1) → M'
  80. Translate(Q, n_1) → Q'
  81. Translate(O, n_1) → O'
  82. Translate(P, n_1) → P'
  83. Translate(R, n_1) → R'
  84. Translate(S, n_1) → S'
  85. Translate(T, n_1) → T'
  86. Translate(D, n_1) → D'_1
  87. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], D'_1) → V'
  88. Vector(V, V') → p_1
  89. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], E'_1) → V'_1
  90. Vector(V, V'_1) → q_1
  91. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], F'_1) → V'_2
  92. Vector(V, V'_2) → r_1
  93. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], G'_1) → V'_3
  94. Vector(V, V'_3) → s_1
  95. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], H'_1) → V'_4
  96. Vector(V, V'_4) → t_1
  97. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], I'_1) → V'_5
  98. Vector(V, V'_5) → u_2
  99. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], J'_1) → V'_6
  100. Vector(V, V'_6) → v_2
  101. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], K') → V'_7
  102. Vector(V, V'_7) → w_2
  103. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], L') → V'_8
  104. Vector(V, V'_8) → a_2
  105. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], M') → V'_9
  106. Vector(V, V'_9) → b_2
  107. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], Q') → V'_{10}
  108. Vector(V, V'_{10}) → c_2
  109. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], O') → V'_{11}
  110. Vector(V, V'_{11}) → d_2
  111. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], P') → V'_{12}
  112. Vector(V, V'_{12}) → e_2
  113. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], R') → V'_{13}
  114. Vector(V, V'_{13}) → f_2
  115. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], S') → V'_{14}
  116. Vector(V, V'_{14}) → g_2
  117. Dilate(V, If[1 < i ≤ 2, 2 - i, 0], T') → V'_{15}
  118. Vector(V, V'_{15}) → h_2