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3D Vectors and Parabolas

3D Vectors and Parabolas
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2019-02-07 04:22
VectorSolid GeometryCalculus
This example demonstrates the transformation of vectors in 3D space and the properties of parabolas. Key mathematical concepts include vectors, parabolas in 3D space, and linear transformations of vectors. Using commands like ApplyMatrix and OrthogonalPlane, users can visually understand how vector transformations affect parabolas in 3D space. Suitable for high school and above students or teachers.

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. Translate(Vector[(-t_{2})], (2 * D)) → g
  18. Point((0, 0, 0), t_{2}) → E
  19. Translate(Vector[(-t_{2})], (2 * D) - E) → h