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Vector Projection

Vector Projection
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2016-09-02 11:27
VectorCoordinate GeometryGeometric Construction
This example demonstrates the process of vector projection. Key mathematical concepts include vector addition and projection. Using GeoGebra commands such as Line, Ray, OrthogonalLine, Vector, and Intersect, the projection of vectors can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(B, C) → r
  2. Ray(C, B) → h
  3. OrthogonalLine(A, h) → i
  4. If(a ≟ 0 ∨ a ≟ 1, "", If[a ≟ -1, "-", "" + a]) → a1
  5. If(c ≟ 0 ∨ c ≟ 1, "", If[c ≟ -1, "-", "" + c]) → c1
  6. If(d ≟ 1, "+", If[d ≟ -1, "-", If[(d > 1) ∧ c ≟ 0, "" + d, If[(d > 1) ∧ (c ≠ 0), "+" + d, "" + d]]]) → d1
  7. If(b ≟ 1, "+", If[b ≟ -1, "-", If[(b > 1) ∧ a ≟ 0, "" + b, If[(b > 1) ∧ (a ≠ 0), "+" + b, "" + b]]]) → b1
  8. If(a ≟ 0, "", text3) → a11
  9. If(b ≟ 0, "", text4) → b11
  10. If(c ≟ 0, "", text5) → c11
  11. If(d ≟ 0, "", text6) → d11
  12. Vector(C, A) → u
  13. Vector(C, B) → v
  14. Ray(C, A) → f
  15. OrthogonalLine(B, f) → k
  16. Intersect(i, r) → D
  17. Segment(A, D) → g
  18. Angle(A, D, C) → α
  19. Vector(C, D) → w
  20. Angle(C, D, A) → β
  21. FractionText(l / n) → text18
  22. FractionText(o / n) → text19
  23. If((c ≠ 0) ∧ (d > 0), "+", "") → sig
  24. Midpoint(C, A) → E
  25. Midpoint(C, B) → F

AI Drawing Prompt Reference

Draw a vector projection diagram with vectors u and v, and their projection vector w. First, draw vectors u and v, then draw the perpendicular line i to vector u through point C, followed by the line r through vector v, find the intersection D, connect AD to get the projection vector w, and finally label the angles α between w and u, and β between w and v.
The prompt above was compiled from the original drawing commands and is for reference only.