向量属性演示

向量属性演示
几何画板及绘图内容加载中,请稍等……
2018-04-27 03:36
①本范例通过动态演示向量的基本属性,如加减法、数乘和模长;②涉及核心数学概念包括向量运算、线性函数、解析几何;③构造中运用了Vector、Point、If等GeoGebra命令及对象,如l_2、k_1、w_1等向量与点对象,以及条件判断If;④适合高中及以上学生及数学爱好者学习向量性质和几何应用。

GeoGebra 命令及参数

  1. Vector(l_2InitPt, l_2TermPt) → l_2
  2. Vector(k_2InitPt, k_2TermPt) → k_2
  3. Vector(n_1InitPt, n_1TermPt) → n_1
  4. Vector(f_1InitPt, f_1InitPt + (r * n_1)) → f_1
  5. Vector(wInitPt, wTermPt) → w
  6. Vector(w_1InitPt, w_1TermPt) → w_1
  7. Vector(k_1InitPt, k_1InitPt + k_2) → k_1
  8. Vector(k_1InitPt, k_1InitPt + (r * k_1)) → k_1ScaleMult
  9. Point(k_1InitPt, k_1ScaleMult) → k_1ScaleMultTermPt
  10. Vector(k_1InitPt + k_2, k_1InitPt + k_2 + l_2) → l_1
  11. Vector(l_1InitPt, l_1InitPt + (r * l_1)) → l_1ScaleMult
  12. Point(l_1InitPt, l_1ScaleMult) → l_1ScaleMultTermPt
  13. Vector(lInitPt, lTermPt) → l
  14. Vector(uInitPt, uTermPt) → u
  15. Vector(vInitPt, vTermPt) → v
  16. Vector(qInitPt, qTermPt) → q
  17. Vector(mInitPt, mTermPt) → m
  18. Vector(nInitPt, nTermPt) → n
  19. Vector(dInitPt, dTermPt) → d
  20. Vector(fInitPt, fTermPt) → f
  21. Vector(gInitPt, gTermPt) → g
  22. Vector(hInitPt, hTermPt) → h
  23. If(b, ¬c) → i
  24. If(b, ¬c) → j
  25. Vector(lInitPt, lTermPt + (r * l)) → lScaleMult
  26. Vector(pInitPt, pTermPt) → p
  27. Vector(u_1InitPt, u_1TermPt) → u_1
  28. Vector(v_1InitPt, v_1TermPt) → v_1
  29. Vector(a_1InitPt, a_1TermPt) → a_1
  30. Vector(b_1InitPt, b_1InitPt + v_1) → b_1
  31. Vector(c_1InitPt, c_1InitPt + w_1) → c_1
  32. Vector(g_1InitPt, g_1InitPt + (s * n_1)) → g_1
  33. Vector(p_1InitPt, p_1InitPt + ((r + s) * n_1)) → p_1
  34. Vector(C, C + (r * l)) → vScaleMult
  35. Vector(k_1InitPt, k_1InitPt + l_1 + k_1) → m_1
  36. Vector(m_1InitPt, m_1InitPt + (r * m_1)) → m_1ScaleMult
  37. Point(m_1InitPt, m_1ScaleMult) → m_1ScaleMultTermPt
  38. Vector(e_1InitPt, e_1TermPt) → e_1
  39. Vector(t_1InitPt, t_1TermPt) → t_1
  40. Vector(u_2InitPt, u_2TermPt) → u_2
  41. Vector(v_2InitPt, v_2TermPt) → v_2
  42. Vector(r_1InitPt, r_1TermPt) → r_1
  43. Vector(s_1InitPt, s_1TermPt) → s_1
  44. Vector(w_2InitPt, w_2TermPt) → w_2
  45. Vector(a_2InitPt, a_2TermPt) → a_2
  46. Vector(b_2InitPt, b_2TermPt) → b_2
  47. Vector(c_2InitPt, c_2TermPt) → c_2
  48. Vector(d_2InitPt, d_2TermPt) → d_2
  49. Vector(f_2InitPt, F) → f_2
  50. Vector(g_2InitPt, D) → g_2
  51. Vector(e_2InitPt, e_2InitPt + (s * d_2)) → e_2
  52. Vector(h_2InitPt, h_2InitPt + d_2) → h_2
  53. Vector(i_2InitPt, i_2TermPt) → i_2
  54. Vector(j_2InitPt, j_2TermPt) → j_2
  55. Vector(q_1InitPt, q_1InitPt + k_2) → q_1
  56. Vector(q_1InitPt, K + l_2) → m_2
  57. Vector(b_1InitPt, c_1TermPt) → p_2
  58. Vector(q_2InitPt, q_2InitPt + (r * m_2)) → q_2
  59. Vector(b_1InitPt, c_1TermPt) → r_2
  60. Vector(s_2InitPt, s_2InitPt + w_1) → s_2
  61. Vector(t_2InitPt, t_2InitPt + v_1) → t_2
  62. Point(s_2InitPt, w_1) → s_2TermPt
  63. Point(t_2InitPt, v_1) → t_2TermPt
  64. Vector(s_2InitPt, t_2TermPt) → u_3
  65. Vector(q_1InitPt + k_2, K + l_2) → n_2
  66. Vector(w_3InitPt, w_3InitPt + p) → w_3
  67. Point(w_3InitPt, p) → w_3TermPt

AI 绘图提示语参考

画一个动态演示向量性质的图形,展示向量加法、标量乘法和模长的关系。包含多个向量,通过滑块控制大小和方向,并用点标记关键位置。先画出基础向量,然后通过向量运算生成新的向量,并用标量乘法调整长度,最后将所有元素组合展示向量几何性质。
以上提示语为根据原始绘图命令整理而来,仅供参考。