MathPlotAI Logo MathPlotAI

Vector Dot Product Distributive Law Demo

Vector Dot Product Distributive Law Demo
Loading the math board and drawing, please wait…
2019-06-22 17:35
VectorGeometric Construction
This example dynamically demonstrates the distributive law of the dot product for vectors: (u+v).w = u.w + v.w. It involves core math concepts like vector dot product, vector addition, and linear operations. Key GeoGebra commands used include Polygon, Point, Segment, Vector, Angle, with conditional logic (If) and polyline (PolyLine) for auxiliary constructions. Slider animations (Slider) allow interactive adjustment of vector magnitudes and directions. Suitable for high school students and university introductory courses in vector algebra and linear algebra.

GeoGebra Commands & Parameters

  1. Polygon((0, 0), (0, 0) + (4, 0), (0, 0) + (4, 4.5), (0, 0) + (0, 4.5)) → V, g, i, j, k
  2. Point(xAxis) → E_0
  3. PointIn(V) → C
  4. Segment((0, 0), C) → c
  5. PointIn(V) → B
  6. Point(c) → S_2
  7. PolyLine((0, 0), B, C) → p
  8. Point(p) → S_1
  9. If(wp, S_1, S_2) → S
  10. Vector((0, 0), (0, y(A))) → f
  11. Vector((0, 0), (0, 0) + (0, -1.72 / 2)) → v_x
  12. Segment(B, C) → b
  13. Segment((0, 0), B) → a
  14. Vector((0, 0), S_2) → s
  15. If(h_0 ≤ y(B), S_1, B) → D
  16. Vector((0, 0), D) → s_1
  17. Vector(B, S_1) → s_2
  18. Angle(s_1, f) → β
  19. Point(xAxis) → E_2
  20. Point(xAxis) → E_1
  21. Segment(E_1, E_1 + (0, y(B))) → h_1
  22. Point(xAxis) → E_3
  23. Segment((Min[x(S_2), x(S_1)], y(S)), E_0 + (0, y(S))) → level
  24. Segment((x(B), y(B)), E_0 + (0, y(B))) → level_2
  25. Segment(C, E_0 + (0, y(C))) → level_3
  26. Segment((x(E_2), y(B)), E_2 + (0, y(S))) → h_2
  27. Segment(E_3, E_3 + (0, y(S))) → h
  28. Angle(Vector[B, B + (1, 0)], s_2) → γ
  29. Angle(s, f) → α
  30. Vector(S, S + (0, f_1 / 2)) → f_2
  31. If(y(C) ≥ y(B), "", "<0") → vzh

AI Drawing Prompt Reference

Draw a dynamic illustration showing the distributive law of the dot product for vectors (u+v).w = u.w + v.w. Include three vectors u, v, and w, visualizing the distributive law through vector addition, dot product, and linear operations. Use sliders to adjust vector magnitudes and directions, and draw auxiliary lines and angle markings to clearly show the calculation process and geometric relationships.
The prompt above was compiled from the original drawing commands and is for reference only.