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Vector-Based Tetrahedron Proof

Vector-Based Tetrahedron Proof
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2019-04-21 09:52
VectorSolid GeometryGeometric Construction
This example demonstrates a proof of a tetrahedron using vector methods. Key math concepts include vector operations, magnitude of vectors, dot product, and the volume formula of a tetrahedron. It utilizes GeoGebra commands like Intersect, Point, Tetrahedron, Midpoint, Vector, Segment, and Angle. Suitable for high school students and above to learn about solid geometry and vector mathematics.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, zAxis) → B
  2. Point(xAxis) → C
  3. Point(Circle[Midpoint[B, C], (Distance[B, C] * sqrt(3) / 2), Segment[B, C]]) → D
  4. Tetrahedron(B, C, D) → a, A, edgeCD, edgeBD, faceABC, faceACD, faceABD, faceBCD, edgeAC, edgeAB, edgeBC, edgeAD
  5. Midpoint(D, C) → M
  6. Vector(B, M) → u
  7. Vector(A, M) → v
  8. Midpoint(B, D) → E
  9. Midpoint(B, C) → F
  10. Segment(F, D) → f
  11. Segment(C, E) → g
  12. Intersect(f, g) → G
  13. Segment(G, A) → h
  14. Angle(B, M, A) → α