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Vector Subtraction: Dynamic Geometric Illustration

Vector Subtraction: Dynamic Geometric Illustration
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2016-03-30 06:15
AngleVectorTransformationGeometric ConstructionSlider Animation
In collections Vector Operations Vector Operations
This GeoGebra example dynamically and geometrically illustrates vector subtraction, showing that vector a minus vector b equals vector a plus the opposite of vector b, and demonstrating the triangle law or parallelogram law of vector addition. Core mathematical concepts include vector subtraction, opposite vectors, vector addition, triangle law, parallelogram law, and translation/rotation of vectors in the plane. Construction highlights: using GeoGebra commands such as Mirror to generate the opposite of vector b, Dilate, Translate, and Rotate to construct the difference vector, Vector to draw vectors, and Textfield/InputBox for interactive input, with a button to trigger dynamic updates. Objects include points A, B, C and their mirrored images, vectors u, v, w, etc. Suitable for high school or early college students learning vector operations, and for teachers demonstrating the geometric essence of vector subtraction, with connections to right triangles, hyperbolas, and angles, though the core focus is on vector arithmetic.

GeoGebra Commands & Parameters

  1. Mirror(B, A) → B'_1
  2. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], C) → A'_1
  3. Vector(A, A'_1) → w
  4. Translate(B'_1, w) → F
  5. Vector(A, B) → v
  6. Vector(A, C) → u
  7. Rotate(C, If[0 < a ≤ 1, ((a * 180))°, 180°], A) → C'
  8. Dilate(A, If[1 < a < 2, 2 - a, 1], B) → A'
  9. Vector(A, A') → b
  10. Rotate(C, 180°, A) → C'_1
  11. Translate(C'_1, b) → D
  12. Translate(C'_1, v) → E
  13. Vector(A, E) → f
  14. Textfield() → InputBox1
  15. Translate(B, w) → B'
  16. Vector(A'_1, B') → c
  17. Dilate(A, If[1 < a ≤ 2, 2 - a, 0], F) → A'_2
  18. Vector(A, A'_2) → d
  19. Vector(A, B) → e
  20. Dilate(A, If[0 < g ≤ 1, 1 - g, 0], B) → A'_3
  21. Vector(A, A'_3) → h
  22. Translate(C, h) → C'_2
  23. Vector(A, C) → j
  24. Dilate(A, If[1 < g ≤ 2, 2 - g, 0], C'_2) → A'_4
  25. Dilate(A, If[-1 < a ≤ 0, (-a), 0], B'_1) → A'_5
  26. Vector(A, A'_5) → l
  27. Vector(A'_1, F) → m
  28. Vector(A, B'_1) → n
  29. Mirror(C, A) → C'_3
  30. Dilate(A, If[-1 < g ≤ 0, (-g), 0], C'_3) → A'_6
  31. Vector(A, A'_6) → i
  32. Vector(A, C'_3) → p
  33. Translate(A'_6, h) → G
  34. Vector(A'_3, G) → q
  35. Dilate(A, If[1 < g ≤ 2, 2 - g, 0], G) → A'_7
  36. Vector(A, A'_7) → k

AI Drawing Prompt Reference

Create a dynamic geometric illustration showing vector subtraction. Place three points on a plane as the origin and endpoints of two vectors, drawing arrows for the original vectors. Reflect one vector about the origin to obtain its opposite. Construct the difference vector by translating and rotating, making it equal to the first vector plus the opposite of the second. Include auxiliary points, translated vectors, and triangles or parallelograms formed by these vectors to visually demonstrate the triangle law and parallelogram law. Add a slider or input box to dynamically adjust parameters, updating the figure to show different cases of vector subtraction.
The prompt above was compiled from the original drawing commands and is for reference only.