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向量变换与平面

向量变换与平面
几何画板及绘图内容加载中，请稍等……
2019-02-07 04:52
向量解析几何
该范例演示了如何使用向量变换和平面来构造几何图形。核心数学概念包括向量、坐标和变换。通过ApplyMatrix、OrthogonalPlane等命令，用户可以理解向量在二维空间中的变换及其对几何图形的影响。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. ApplyMatrix(M, e_{1}) → t_{1}
  2. ApplyMatrix(M, e_{2}) → t_{2}
  3. ApplyMatrix(M, e_{3}) → t_{3}
  4. OrthogonalPlane((0, 0, 0), Vector[t_{1} ⊗ t_{2}]) → d
  5. OrthogonalPlane((0, 0, 0), Vector[t_{1} ⊗ t_{3}]) → e
  6. OrthogonalPlane((0, 0, 0), Vector[t_{2} ⊗ t_{3}]) → f
  7. OrthogonalPlane(P, Vector[u ⊗ v]) → a
  8. PointIn(a) → B
  9. ApplyMatrix(M, B) → B'
  10. Sequence(Sequence[(n - (2 * w) + t, w, t), w, -4, 4, 1], t, -4, 4, 1) → m1
  11. ApplyMatrix(M, m1) → m1'
  12. Sequence(Sequence[Sequence[(x_{1}, x_{2}, x_{3}), x_{1}, -4, 4, 1], x_{2}, -4, 4, 1], x_{3}, -4, 4, 1) → l1
  13. ApplyMatrix(M, l1) → l1'
  14. ApplyMatrix(M, C) → C'
  15. Point((0, 0, 0), t_{1}) → D
  16. Translate(t_{1}, D) → c
  17. Point((0, 0, 0), t_{2}) → E
  18. Translate(Vector[(-t_{2})], (4 * D)) → g
  19. Translate(Vector[(-t_{2})], (4 * D) - E) → h
  20. Translate(t_{1}, (2 * D)) → i
  21. Translate(t_{1}, (3 * D)) → j
  22. Sequence((4 - t, -2 - t, t), t, -4, 4, 0.5) → l2
  23. ApplyMatrix(M, l2) → l2'