MathPlotAI Logo MathPlotAI

Bound Vectors Demo

Bound Vectors Demo
Loading the math board and drawing, please wait…
2019-02-26 00:21
VectorGeometric Construction
This example demonstrates the concept and representation of bound vectors. It involves core mathematical concepts such as vectors, vector operations, magnitude, and direction. Construction highlights include using commands like Vector, If, Sequence, and Segment to create and manipulate vectors. Suitable for high school mathematics education, illustrating vector geometry and operations.

GeoGebra Commands & Parameters

  1. Vector(O, B) → u
  2. Vector(O, C) → v
  3. If(a > 0, floor(a), abs(ceil(a))) → anr
  4. If(b > 0, floor(b), abs(ceil(b))) → bnr
  5. Sequence(Vector[If[a > 0, Vector[O + (i * u), O + ((i + 1) * u)], Vector[O - (i * u), O - ((i + 1) * u)]]], i, 0, anr - 1) → L_1
  6. Sequence(Vector[If[b > 0, Vector[O + (i * v), O + ((i + 1) * v)], Vector[O - (i * v), O - ((i + 1) * v)]]], i, 0, bnr - 1) → L_2
  7. If(a > 0, Vector[O + (anr * u), D], Vector[O - (anr * u), D]) → alast
  8. If(b > 0, Vector[O + (bnr * v), E], Vector[O - (bnr * v), E]) → blast
  9. Vector(O, O + (a * u) + (b * v)) → w
  10. Segment(D, P) → f
  11. Segment(P, E) → g

AI Drawing Prompt Reference

Draw vectors u and v starting from point O, representing directions from O to points B and C respectively. Generate sequences L1 and L2 showing repeated segments in both positive and negative directions of vectors u and v based on parameters a and b. If a and b are positive, extend lines from O along u and v to points D and E respectively. Finally, draw a line from O to point F along the linear combination of u and v, and connect D to F and F to E with straight lines.
The prompt above was compiled from the original drawing commands and is for reference only.