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向量与分量练习

向量与分量练习
几何画板及绘图内容加载中，请稍等……
2014-06-28 23:34
向量解析几何几何作图
①本范例演示如何通过交互式测试找到向量的分量；②涉及的核心数学概念包括向量分解、坐标几何和勾股定理；③构造要点：使用了Shuffle, Element, Textfield, Corner, onboardingTextOffset, Polygon, Segment, Vector, Translate等GeoGebra命令和对象；④适合高中阶段学习向量与解析几何的学生使用。

GeoGebra 命令及参数

  1. Shuffle({1, 2, 3, 4, 5, 6, 7}) → allCaseNum, {6, 7, 5, 1, 2, 3, 4}
  2. Shuffle(Sequence[t, t, -6, 6, 1] \ {-1, 1}) → allCompX, {-3, -4, -2, -5, 3, 6, 2, -6, 5, 4, 0}
  3. Shuffle(Sequence[t, t, -6, 6, 1] \ {0, -1, 1}) → allCompY, {-2, -4, -5, 2, -6, 5, 6, 4, -3, 3}
  4. Shuffle(Join[Sequence[Sequence[(j, k), j, -4, 4, 1], k, -4, 4, 1]]) → startGrid, {(1, -2), (-4, 3), (-2, -3), (-3, 1), (-4, -3), (-2, -1), (-2, 2), (4, 0), (-3, 3), (2, 1), (-1, -3), (1, 1), (4, -4), (2, -3), (2, 0), (0, 3), (-2, -4), (0, 2), (-1, -4), (-3, -3), (-2, -2), (3, 2), (1, 0), (4, -3), (0, 0), (0, -2), (-4, 4), (2, -4), (-1, -1), (3, 0), (-1, 0), (0, -3), (2, -2), (4, -1), (-1, 1), (-1, 3), (3, 1), (-4, 1), (3, -3), (4, 1), (1, -1), (1, 3), (1, -4), (-4, 2), (4, 2), (-1, 2), (1, 4), (-1, -2), (-3, -1), (-2, 0), (2, 2), (4, -2), (-2, 3), (2, 3), (-4, -2), (-4, -4), (2, -1), (3, -2), (3, -4), (-3, 0), (4, 3), (-3, -4), (1, 2), (0, 1), (4, 4), (-3, -2), (0, -1), (-1, 4), (0, -4), (-2, 4), (3, 3), (2, 4), (-3, 4), (-4, 0), (-4, -1), (-2, 1), (3, 4), (-3, 2), (3, -1), (1, -3), (0, 4)}
  5. Element(allCaseNum, Mod[countQuestion, Length[allCaseNum]] + 1) → caseNum
  6. Element(allCompX, Mod[countQuestion, Length[allCompX]] + 1) → compX
  7. Element(allCompY, Mod[countQuestion, Length[allCompY]] + 1) → compY
  8. Element(startGrid, Mod[countQuestion, Length[startGrid]] + 1) → V1
  9. Textfield(inputB) → InputBoxB
  10. Corner(5) → layoutAppSize
  11. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], onboardingCase, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  12. Textfield(inputA) → InputBoxA
  13. Textfield(inputC) → InputBoxC
  14. Polygon(P1, Mirror[P1, yAxis], Mirror[P1, (0, 0)], Mirror[P1, xAxis]) → peep, p1, f, g, h
  15. Segment((-10.8, 0), (10.8, 0)) → fakeX
  16. Segment((0, -10.8), (0, 10.8)) → fakeY
  17. Vector(V1, V2) → givenVec
  18. Vector(V1, (0, 0)) → aniVec
  19. Translate(V1, Vector[(aniSli * aniVec)]) → V1T
  20. Translate(V2, Vector[(aniSli * aniVec)]) → V2T
  21. Vector(V1T, V2T) → transVec
  22. Segment(V2T, (0, y(V2T))) → projY
  23. Segment(V2T, (x(V2T), 0)) → projX
  24. Segment((compX, 0), (0, 0)) → segmX
  25. Segment((0, compY), (0, 0)) → segmY

AI 绘图提示语参考

在坐标系中绘制一个向量，起点为原点，终点为随机选择的点，并显示该向量的x和y分量。先画出坐标轴，然后随机选择一个点作为向量的终点，并画出向量。接着，从向量的终点向x轴和y轴分别作垂线，交点分别为x分量和y分量的终点。最后，画出x分量和y分量，并标注它们的长度。
以上提示语为根据原始绘图命令整理而来，仅供参考。