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Vectors as Linear Combinations of a Basis

Vectors as Linear Combinations of a Basis
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2019-12-02 22:47
VectorCoordinate GeometryGeometric Construction
This example demonstrates how any vector in the plane can be expressed as a linear combination of two independent vectors. Key math concepts include vectors, linear combinations, and basis. It is constructed using GeoGebra commands like Vector, Line, Intersect, Segment, and Translate, making it suitable for high school students learning vector space fundamentals.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → w
  3. Vector(A, D) → v
  4. Line(A, B) → a
  5. Line(A, D) → b
  6. Line(C, a) → c
  7. Line(C, b) → d
  8. Intersect(a, d) → E
  9. Intersect(b, c) → F
  10. Vector(A, E) → u'
  11. Vector(A, F) → v'
  12. Segment(E, C) → f
  13. Segment(F, C) → g
  14. Vector(G, H) → z
  15. Translate(I, h) → I'
  16. Vector(I, I') → i

AI Drawing Prompt Reference

Draw vectors u and w, and their basis vector v. Construct two lines a and b using v, which intersect u and w at points E and F respectively. Connect points E and C, F and C to form segments f and g. Use vector z and h to create vector i.
The prompt above was compiled from the original drawing commands and is for reference only.