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Vector Addition & Commutativity: Geometric Illustration

Vector Addition & Commutativity: Geometric Illustration
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2018-02-08 00:09
VectorTrigonometryCoordinate GeometryCalculusGeometric Construction
This example geometrically illustrates vector addition and its commutativity. Key math concepts involved include vectors, vector addition, geometric representation, and commutativity. The construction utilizes GeoGebra commands/objects such as Vector, Rotate, Dilate, Translate, and Textfield. Suitable for high school and above students to understand the intuitive meaning and properties of vector operations.

GeoGebra Commands & Parameters

  1. Vector(A, B) → v
  2. Vector(A, C) → u
  3. Rotate(C, If[0 < a ≤ 1, ((a * 180))°, 180°], A) → C'
  4. Dilate(A, If[1 < a < 2, 2 - a, 1], B) → A'
  5. Vector(A, A') → b
  6. Rotate(C, 180°, A) → C'_1
  7. Translate(C'_1, b) → D
  8. Translate(C'_1, v) → E
  9. Vector(A, E) → f
  10. Textfield() → InputBox1
  11. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'_1
  12. Vector(A, A'_1) → w
  13. Translate(B, w) → B'
  14. Vector(A'_1, B') → c
  15. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], B') → A'_2
  16. Vector(A, A'_2) → d
  17. Vector(A, B) → e
  18. Dilate(A, If[0 < g ≤ 1, 1 - g, 0], B) → A'_3
  19. Vector(A, A'_3) → h
  20. Translate(C, h) → C'_2
  21. Vector(A'_3, C'_2) → i
  22. Vector(A, C) → j
  23. Dilate(A, If[1 < g ≤ 2, 2 - g, 0], C'_2) → A'_4
  24. Vector(A, A'_4) → k