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向量形式：直线与平面

向量形式：直线与平面
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2017-06-13 11:07
向量解析几何立体几何几何作图
①本范例演示了三维空间中直线与平面的向量表示方法及可视化；②涉及核心数学概念包括向量、点积、法向量、直线参数方程、平面方程等；③作图要点：使用Vector、Plane、PointIn、Line、Sequence、Point等GeoGebra命令构建几何对象，通过参数化展示直线与平面的动态关系；④适合高中及以上学生及需要立体几何可视化的学习者。

GeoGebra 命令及参数

  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