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Vector Subtraction Demonstration by Zach Schaver

Vector Subtraction Demonstration by Zach Schaver
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2019-02-17 04:27
VectorCoordinate GeometryGeometric Construction
This example demonstrates vector subtraction in two-dimensional space, visually showing the result of subtracting one vector from another. The core mathematical concepts involved include vectors, geometric representation, coordinate transformation, and geometric construction. It utilizes GeoGebra commands and objects such as Vector, Dilate, Line, Intersect, Rotate, and Point to construct vectors, calculate intersections, and display geometric relationships. Suitable for high school students learning about the geometric meaning of vector operations and for teaching demonstrations combining vectors with geometry.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(C, D) → v
  3. Dilate(A, If[0 ≤ a < 1, 1 - a, 0], E) → A'
  4. Line(A, A') → f
  5. Line(B, f) → g
  6. Line(A', u) → h
  7. Intersect(g, h) → F
  8. Vector(A', F) → u'
  9. Dilate(C, If[1 ≤ a < 2, 2 - a, 0], F) → C'
  10. Line(C', C) → i
  11. Line(C', v) → j
  12. Line(D, i) → k
  13. Intersect(j, k) → G
  14. Vector(C', G) → v'
  15. Rotate(v', If[2 ≤ a ≤ 3, ((2 - a) * 180°), 180°], E) → v''
  16. Point(v'') → H
  17. Dilate(E, If[3 ≤ a < 4, 4 - a, 0], H) → E'
  18. Vector(E, E') → w
  19. Dilate(C, If[0 ≤ b < 1, 1 - b, 0], I) → C''
  20. Line(C, C'') → l
  21. Line(C'', v) → m
  22. Line(D, l) → n
  23. Intersect(m, n) → J
  24. Vector(C'', J) → c
  25. Dilate(A, If[1 ≤ b < 2, 2 - b, 0], J) → A''
  26. Line(A, A'') → p
  27. Line(A'', u) → q
  28. Line(B, p) → r
  29. Intersect(q, r) → K
  30. Vector(A'', K) → d
  31. Rotate(d, If[2 ≤ b ≤ 3, ((-(2 - b)) * 180°), 180°], A'') → d'
  32. Point(d') → L
  33. Dilate(I, If[3 ≤ b < 4, 4 - b, 0], L) → I'
  34. Vector(I, I') → e