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Parametric Vector Equation of the Plane

Parametric Vector Equation of the Plane
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2014-02-16 21:17
VectorCoordinate GeometrySolid Geometry
This example demonstrates the geometric representation of the parametric vector equation of a plane. Key math concepts include vectors, three-dimensional space, and parametric equations. Construction highlights from the GeoGebra command summary involve commands like Vector, OrthogonalLine, Textfield, Polygon, and Translate. Suitable for high school and above students learning spatial geometry and vector concepts.

GeoGebra Commands & Parameters

  1. Vector(O, X) → i
  2. Vector(O, Z) → k
  3. OrthogonalLine(Rotate, yAxis) → a_1
  4. OrthogonalLine(Rotate, xAxis) → b_1
  5. Vector(O, Y) → j
  6. Textfield(a_x) → inputBox1
  7. Textfield(a_y) → inputBox2
  8. Textfield(a_z) → inputBox3
  9. Textfield(b_x) → inputBox4
  10. Textfield(b_y) → inputBox5
  11. Textfield(b_z) → inputBox6
  12. Textfield(c_x) → inputBox7
  13. Textfield(c_y) → inputBox8
  14. Textfield(c_z) → inputBox9
  15. Vector(O, A) → a
  16. Vector(A, B) → b
  17. Vector(A, C) → c
  18. Vector(A, B_1) → λb
  19. Vector(B_1, P) → μc
  20. Vector(O, Bunit) → bunit
  21. Vector(O, Cunit) → cunit
  22. Polygon(K, L, M, N) → poly1, k_1, l, m, n
  23. Vector(O, P) → r
  24. Translate(O, k) → O'
  25. Vector(O, O') → u
  26. Translate(O, k) → O'_1
  27. Vector(O, O'_1) → v

AI Drawing Prompt Reference

In a 3D coordinate system, draw a plane defined by a point A and two direction vectors b and c. From the origin O, draw unit vectors i, j, k along the x, y, and z axes. On the plane, select points B and C such that vector AB equals b and AC equals c. Through point A, draw two auxiliary lines parallel to the y-axis and x-axis for orientation. Construct a parallelogram on the plane with vertices determined by A, B, C, and their linear combinations, showing vectors λb and μc from A, and the position vector r from O to a point P on the plane. Also, at the origin, draw two translated vectors representing the plane's directions. Add nine input boxes for the components of vectors a, b, and c to dynamically adjust the plane.
The prompt above was compiled from the original drawing commands and is for reference only.