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Vector Subtraction: Dynamic Demonstration of Parallelogram and Triangle Rules

Vector Subtraction: Dynamic Demonstration of Parallelogram and Triangle Rules
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2016-12-20 12:56
VectorTransformationGeometric ConstructionSlider Animation
In collections Vector Basics
① This GeoGebra example dynamically demonstrates the subtraction of two vectors u and v (u−v and v−u), visually illustrating the geometric meaning of vector subtraction. ② The core mathematical concept is vector subtraction, which is equivalent to adding the opposite vector, and can be constructed using the parallelogram rule or the triangle rule. ③ Construction highlights: The Vector command creates vectors u and v, Point defines start points A and B, Translate is used to build the parallelogram, Rotate assists auxiliary construction, and If controls conditional display; objects include A, B, u', D, C, v', b, t_1, E, TransUV, C', D', a, t_2, F, TransVU, A', B', v, u, button1, text1, text1_1, D'', e, I, f, J, UV, v'', B'', c, G, u'', g, K, VU, button2, Show, ShowBoth_1, with buttons and text to toggle between the two subtraction results. ④ Suitable for high school plane vector lessons or introductory linear algebra, helping students understand the direction and magnitude of vector subtraction and its geometric construction.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u'
  2. Vector(C, D) → v'
  3. Segment(B, C) → b
  4. Point(b, 1 - t_1) → E
  5. Vector(C, E) → TransUV
  6. Translate(C, TransUV) → C'
  7. Translate(D, TransUV) → D'
  8. Segment(A, D) → a
  9. Point(a, t_2) → F
  10. Vector(A, F) → TransVU
  11. Translate(A, TransVU) → A'
  12. Translate(B, TransVU) → B'
  13. Vector(C', D') → v
  14. Vector(F, B') → u
  15. Rotate(D', 180°, E) → D''
  16. Segment(D'', E) → e
  17. Point(e, 2 - t_1) → I
  18. Segment(D'', A) → f
  19. Point(f, 3 - t_1) → J
  20. Vector(A, J) → UV
  21. Vector(E, I) → v''
  22. Rotate(B', 180°, D) → B''
  23. Segment(D, B'') → c
  24. Point(c, t_2 - 1) → G
  25. Vector(D, G) → u''
  26. Segment(C, B'') → g
  27. Point(g, t_2 - 2) → K
  28. Vector(C, K) → VU
  29. If(Show ≟ true, t_1, 0) → ShowBoth_1
  30. If(Show ≟ true, t_2, 0) → ShowBoth_2

AI Drawing Prompt Reference

Draw two dynamic vectors u and v, demonstrating their subtraction u-v and v-u, visually illustrating the geometric meaning of vector subtraction through the parallelogram and triangle rules. Start by plotting the initial points of vectors u and v, then construct u-v using the parallelogram rule and v-u using the triangle rule. Include a slider to control the display and buttons to toggle between the two subtraction results.
The prompt above was compiled from the original drawing commands and is for reference only.