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Distance Between Parallel Planes

Distance Between Parallel Planes
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2015-07-31 21:07
VectorCoordinate GeometryGeometric Construction
This example demonstrates calculating the distance between two parallel planes and its geometric significance. Key mathematical concepts include vectors, plane equations, and distance formulas. Construction involves GeoGebra commands like OrthogonalLine, Line, Intersect to establish plane and vector relationships. Suitable for high school students studying analytic geometry or mathematical modeling.

GeoGebra Commands & Parameters

  1. OrthogonalLine(O, yAxis, space) → a
  2. Line(O, Unit) → l
  3. Intersect(l, Π_1) → A
  4. Intersect(l, Π_2) → B
  5. Segment(O, A) → d_1
  6. Segment(O, B) → d_2
  7. Vector(A, (2.56, -0.51, 1.54)) → n_1
  8. Vector(B, (-0.58, 0.12, -0.35)) → n_2
  9. Angle(l, Π_1) → α
  10. Angle(l, Π_2) → β
  11. LaTeX(Π_1, true, true) → text1
  12. LaTeX(Π_2, true, true) → text2
  13. PointIn(Π_2) → F
  14. PointIn(Π_1) → G
  15. Midpoint(d_1) → H
  16. Midpoint(d_2) → I