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Vector Addition and Subtraction

Vector Addition and Subtraction
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2019-02-16 12:00
VectorTransformationGeometric Construction
This example demonstrates vector addition and subtraction. Key mathematical concepts include the geometric representation and operations of vectors. Using GeoGebra commands such as Dilate (dilation), Segment (segment), Line (line), Vector (vector), Intersect (intersection), Rotate (rotation), etc., a geometric model of vector addition and subtraction can be constructed. Suitable for students at the junior high school level and above to learn basic vector operations.

GeoGebra Commands & Parameters

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