MathPlotAI Logo MathPlotAI

Vector Addition and Commutativity

Vector Addition and Commutativity
Loading the math board and drawing, please wait…
2020-11-18 17:31
VectorFunctionTransformation
This example illustrates vector addition and its commutativity geometrically. It involves core mathematical concepts such as vectors and vector addition. Using GeoGebra commands like Vector, Rotate, Dilate, Translate, etc., the geometric representation of vector addition is constructed. Suitable for students from middle school and above to learn about vector addition and its properties.

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

AI Drawing Prompt Reference

Start from a common point, draw two vectors, one pointing up-right and the other down-right. Through rotations and dilations, construct their sum vector and demonstrate the commutativity of vector addition. The figure includes several auxiliary vectors and points connected by translations and dilations, forming parallelogram structures. Use sliders to animate the process, showing that the order of adding the two vectors does not affect the result.
The prompt above was compiled from the original drawing commands and is for reference only.