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Intersection of 3 Planes at a Point

Intersection of 3 Planes at a Point
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2020-09-30 02:42
VectorCoordinate GeometrySolid GeometryMatrix
This example demonstrates the intersection of three planes at a single point in space. Key math concepts include plane equations, spatial geometry, and linear algebra involving determinants and matrix operations. Construction highlights GeoGebra commands like IntersectPath, Intersect, FractionText, PointIn, Determinant, Invert, and objects such as λ, a, p, b, c, q, r, f, g, A. Suitable for high school and above students learning spatial geometry, linear algebra, and 3D visualization.

GeoGebra Commands & Parameters

  1. IntersectPath(p, q) → f
  2. IntersectPath(q, r) → g
  3. Intersect(f, g) → A
  4. FractionText(A) → text1
  5. PointIn(p) → B
  6. PointIn(r) → C
  7. PointIn(q) → D
  8. Determinant(m1) → d
  9. Invert(m1) → m2
  10. FractionText(d) → text10
  11. FractionText(e) → text12
  12. FractionText(h) → text13
  13. FractionText(i) → text14

AI Drawing Prompt Reference

Draw the intersection point of three planes. First, create three planes p, q, and r. Then, find the intersection line f of p and q, and the intersection line g of q and r. Next, determine the intersection point A of f and g. Finally, show the coordinates of A and select points B, C, and D on planes p, r, and q, respectively.
The prompt above was compiled from the original drawing commands and is for reference only.