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Lines and Planes - Vector Forms

Lines and Planes - Vector Forms
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2017-08-10 20:25
VectorCoordinate GeometryGeometric Construction
This example demonstrates the vector forms of lines and planes. Key mathematical concepts include vectors and coordinate geometry. Using GeoGebra commands such as Vector, Plane, PointIn, etc., lines and planes can be constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Vector(Origin, G) → T1
  2. Plane(A, Origin_B, Origin) → a
  3. PointIn(a) → E
  4. PointIn(a) → Origin_F
  5. Vector(Origin_B, A) → T1_A
  6. Line(qwInitPt, wTermPt) → Line_{2D}
  7. Vector(qwInitPt, wTermPt) → w
  8. Vector(qwInitPt, qwInitPt + (t * w)) → wScl
  9. Vector(O, qwInitPt) → u
  10. Vector(O, qwInitPt + (t * w)) → v
  11. Plane(O, qwInitPt, wTermPt) → n
  12. Vector(qwInitPt, qTermPt) → q
  13. Vector(qwInitPt, qwInitPt + (s * q)) → qScl
  14. Line(qwInitPt, qTermPt) → f_1
  15. Vector(O, qTermPtScl) → v_1
  16. Plane(wTermPt, qwInitPt, qTermPt) → c_1
  17. Sequence(Line[qwInitPt + (t * w), q], t, -15, 15) → qParallelLinesPlane
  18. Sequence(qwInitPt + (t * w), t, -15, 15) → wCoordPts
  19. Sequence(qwInitPt + (s * q), s, -15, 15) → qCoordPts
  20. Sequence(Line[qwInitPt + (s * q), w], s, -15, 15) → wParallelLinesPlane
  21. Sequence(Text[" " + (k), qwInitPt + (k * q)], k, -15, 15) → qAxisNumberList
  22. Vector(wTermPt, wTermPt + Vector[(1, 0, -3)]) → u_1
  23. Vector(wTermPt, wTermPt + Vector[(1, 2, -3)]) → w_1
  24. Vector(wTermPt, wTermPt + Vector[(1, -1, -3)]) → h_1
  25. Point(qwInitPt, Vector[(s * q) + (t * w)]) → GridPt
  26. Sequence(Text[" " + (k), qwInitPt + (k * w)], k, -15, 15) → wAxisNumberList