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w Defined by Basis Vectors u and v

w Defined by Basis Vectors u and v
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2014-02-17 20:15
VectorCoordinate GeometryGeometric Construction
This example demonstrates how the vector w is defined as a linear combination of the basis vectors u and v. Key mathematical concepts include linear combinations of vectors. Construction highlights the use of the Vector, Segment, If, and Sequence commands in GeoGebra. Suitable for high school mathematics education and learning vector concepts.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Vector(A, C') → z
  4. Vector(A, A') → w
  5. Vector(A, B') → c
  6. Segment(B', A') → d
  7. Segment(C', A') → e
  8. If(a > 0, floor(a), abs(ceil(a))) → anr
  9. If(b > 0, floor(b), abs(ceil(b))) → bnr
  10. Sequence(Vector[If[a > 0, Vector[A + (i * u), A + ((i + 1) * u)], Vector[A - (i * u), A - ((i + 1) * u)]]], i, 0, anr - 1) → as
  11. If(a > 0, Vector[A + (anr * u), B'], Vector[A - (anr * u), B']) → alast
  12. Sequence(Vector[If[b > 0, Vector[A + (i * v), A + ((i + 1) * v)], Vector[A - (i * v), A - ((i + 1) * v)]]], i, 0, bnr - 1) → bs
  13. If(b > 0, Vector[A + (bnr * v), C'], Vector[A - (bnr * v), C']) → blast