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Unit Vectors and Normalization

Unit Vectors and Normalization
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2018-12-13 05:07
VectorCoordinate GeometryGeometric Construction
This example demonstrates the concept of unit vectors and their normalization process, visually showing how vector length is adjusted to 1. Core math concepts include vectors, vector magnitude, unit vectors, and normalization. GeoGebra commands and objects used in construction are Intersect, Circle, Point, Vector, Segment, Sphere, PointIn, and Distance. Suitable for high school and above students studying vectors and spatial geometry, or university-level physics education.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Circle(A, 1) → c
  3. Point(c) → C
  4. Vector(A, B) → DYN
  5. Vector(A, C) → UnitVec
  6. Segment(A, (32, 16)) → Vline
  7. Segment(A, B) → DYNline
  8. Intersect(c, DYNline) → UnitDYNInter,
  9. Vector(A, UnitDYNInter) → VectInterCircle
  10. Sphere(A, 1) → g
  11. PointIn(g) → D
  12. Vector(A, D) → u
  13. Distance(D, B) → DB
  14. Segment(A, E) → h
  15. Intersect(h, g) → F,
  16. Vector(A, F) → v
  17. Vector(A, E) → w
  18. Point(c) → G
  19. Vector(A, G) → l
  20. Vector(A, ((m * x(DYN) / Length[DYN]), (m * y(DYN) / Length[DYN]))) → p
  21. Vector(A, ((m * x(DYN) / Length[DYN]), (m * y(DYN) / Length[DYN]))) → q
  22. Point(A, q) → H
  23. Point(A, q) → I
  24. Segment(A, E) → f_1
  25. Intersect(f_1, g) → J,
  26. Vector(A, ((a_1 * x(w) / Length[w]), (a_1 * y(w) / Length[w]), (a_1 * z(w) / Length[w]))) → u_1