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3D Vectors and Geometry Demo

3D Vectors and Geometry Demo
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2021-09-02 13:27
VectorCoordinate GeometrySolid GeometryGeometric Construction
This example demonstrates vector representation, operations, and geometric transformations in three-dimensional space. It involves core math concepts like 3D vectors, vector operations, geometric transformations, and analytical geometry. The construction uses commands/objects such as Vector, Segment, Midpoint, Angle, Line, Point, Intersect, and CircleSector in GeoGebra. Suitable for high school students and math enthusiasts learning about vectors and 3D geometry.

GeoGebra Commands & Parameters

  1. Vector(A, B) → u
  2. Vector(A, C) → v
  3. Vector(A, D) → w
  4. Segment(A, B) → f
  5. Segment(A, C) → g
  6. Segment(A, D) → h
  7. Midpoint(f) → E
  8. Midpoint(g) → F
  9. Midpoint(h) → G
  10. Angle(u, v) → α
  11. Line(A, B) → i
  12. Line(A, C) → j
  13. Point(xAxis) → H
  14. Line(H, yAxis) → k
  15. Intersect(k, i) → I
  16. Intersect(k, j) → J
  17. CircleSector(A, I, J) → c
  18. Point(c) → K
  19. Vector(K, I) → a

AI Drawing Prompt Reference

Draw vectors from point A to points B, C, and D in 3D space, and connect these points with line segments. Find the midpoints of these segments and calculate the angle between the vectors. Draw lines from point A to points B and C. Determine the intersection of the x-axis and y-axis, and draw a line through this intersection. Find the intersections of these lines with the previous lines, and draw a circular sector.
The prompt above was compiled from the original drawing commands and is for reference only.