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Angle Between Vectors by Norm Prokup

Angle Between Vectors by Norm Prokup
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2016-12-11 09:41
AngleVectorTrigonometryCoordinate GeometryGeometric Construction
This example demonstrates how to calculate the angle between two vectors. It involves core mathematical concepts such as vectors, trigonometry, vector magnitude, and dot product. The construction uses GeoGebra commands like CornerThreeD, Polygon, Segment, Sequence, Join, Remove, Point, Vector, Angle, and Distance. Suitable for high school and above mathematics education, focusing on vector and trigonometric applications.

GeoGebra Commands & Parameters

  1. CornerThreeD(-1, 1) → L
  2. CornerThreeD(-1, 7) → U
  3. Polygon((x(L), y(L), 0), (x(L), y(U), 0), (x(U), y(U), 0), (x(U), y(L), 0)) → poly1, f, g, h, i
  4. Segment(O, (0, y(U), 0)) → e
  5. Sequence(Sequence[(p, q, 0), p, ceil(x(L)), floor(x(U)), 1], q, ceil(y(L)), floor(y(U)), 1) → list1
  6. Join(list1) → list2
  7. Remove(list2, {(0, 0, 0)}) → list3
  8. Point(list3) → A
  9. Point(list3) → B
  10. Sequence((x(A), y(A), k), k, ceil(z(L)), floor(z(U)), 1) → list4
  11. Sequence((x(B), y(B), k), k, ceil(z(L)), floor(z(U)), 1) → list5
  12. Point(list4) → C
  13. Point(list5) → D
  14. Vector(O, C) → u
  15. Vector(O, D) → v
  16. Vector((0, 0, 1)) → a
  17. Segment(C, A) → j
  18. Segment(D, B) → k
  19. Angle(D, O, C) → α
  20. Segment(O, A) → l
  21. Segment(O, B) → m
  22. Angle(O, A, C) → β
  23. Angle(O, B, D) → γ
  24. Segment(O, (0, 0, z(U))) → n
  25. Segment(O, (x(U), 0, 0)) → w
  26. Sequence(Segment[(ceil(x(L)), m, 0), (floor(x(U)), m, 0)], m, ceil(y(L)), floor(y(U)), 1) → list7
  27. Sequence(Segment[(n, ceil(y(L)), 0), (n, floor(y(U)), 0)], n, ceil(x(L)), floor(x(U)), 1) → list6
  28. Distance(O, C) → oc
  29. Distance(O, D) → od