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Direction Cosines of a Line

Direction Cosines of a Line
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2019-03-09 14:49
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates the calculation and visualization of direction cosines of a line in 3D space. It involves core mathematical concepts like vectors, angles, and solid geometry. Key GeoGebra commands used include OrthogonalPlane, PointIn, Point, Vector, Angle, OrthogonalLine, Intersect, and Segment. Suitable for high school students and above learning solid geometry and vector mathematics, or for educational demonstrations.

GeoGebra Commands & Parameters

  1. OrthogonalPlane(H, xAxis) → a
  2. PointIn(a) → P
  3. Point(yAxis) → O
  4. Vector(O, P) → L
  5. Point(yAxis) → D
  6. Point(zAxis) → E
  7. Point(xAxis) → F
  8. Angle(F, O, P) → α
  9. Angle(P, O, D) → β
  10. Angle(E, O, P) → γ
  11. OrthogonalLine(P, xAxis, space) → f
  12. OrthogonalLine(P, yAxis, space) → g
  13. OrthogonalLine(P, zAxis, space) → h
  14. Intersect(f, xAxis) → A
  15. Intersect(zAxis, h) → C
  16. Intersect(g, yAxis) → B
  17. Segment(P, A) → i
  18. Segment(P, B) → j
  19. Segment(P, C) → k
  20. Segment(O, A) → l
  21. Segment(O, B) → m
  22. Segment(O, C) → n
  23. Angle(O, A, P) → δ
  24. Angle(P, B, O) → ε
  25. Angle(P, C, O) → ζ