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Geometric Transformations and Vectors

Geometric Transformations and Vectors
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2019-02-07 04:49
VectorComplex NumberTransformation
This example demonstrates geometric transformations and vector operations using GeoGebra. Key mathematical concepts include vectors, transformations, and complex numbers. Using commands like ApplyMatrix and OrthogonalPlane, users can visually understand these concepts. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  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'
  24. Sequence(((-t), (-t), t), t, -4, 4, 0.5) → l3
  25. ApplyMatrix(M, l3) → l3'