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向量叉积的计算

向量叉积的计算
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2016-05-18 15:45
向量立体几何几何作图
①本范例演示了三维空间中两个向量的叉积计算及其几何意义；②涉及的核心数学概念包括向量、三维空间、叉积、向量的模长与方向；③作图要点——使用了Intersect（交点）、Vector（向量）、TableText（文本表格）、Plane（平面）、Angle（角度）、Segment（线段）、LaTeX（公式）等GeoGebra命令与对象；④适合高中及以上学生学习和理解向量运算及立体几何知识。

GeoGebra 命令及参数

  1. Intersect(xAxis, zAxis) → A
  2. Vector(A, B) → u
  3. Vector(A, C) → v
  4. TableText({{LaTeX["\hat{i}"], LaTeX["\hat{j}"], LaTeX["\hat{k}"]}, {LaTeX[(("\textcolor{#000099}{" * x(B)) * "}")], LaTeX[(("\textcolor{#000099}{" * y(B)) * "}")], LaTeX[(("\textcolor{#000099}{" * z(B)) * "}")]}, {LaTeX[(("\textcolor{#CC0000}{" * x(C)) * "}")], LaTeX[(("\textcolor{#CC0000}{" * y(C)) * "}")], LaTeX[(("\textcolor{#CC0000}{" * z(C)) * "}")]}}, "||c") → text2
  5. Plane(A, B, C) → a
  6. Angle(u, crossProduct) → α
  7. Angle(v, crossProduct) → β
  8. Segment((x(crossProduct), y(crossProduct), z(crossProduct)), D) → b
  9. Segment(D, F) → c
  10. Segment(D, E) → d
  11. Segment(B, G) → e
  12. Segment(H, G) → f
  13. Segment(I, G) → g
  14. Segment(C, J) → h
  15. Segment(K, J) → i
  16. Segment(L, J) → j
  17. LaTeX((((((((((((((((((((((((((((((((("\textcolor{#000099}{\vec{u}}\times\textcolor{#CC0000}{\vec{v}}\cr=\text{ }" * text2) * " \cr=\hat{i}[(\textcolor{#000099}{") * y(B)) * "})(\textcolor{#CC0000}{") * z(C)) * "})-(\textcolor{#000099}{") * z(B)) * "})(\textcolor{#CC0000}{") * y(C)) * "})] \cr\text{ }-\hat{j}[(\textcolor{#000099}{") * x(B)) * "})(\textcolor{#CC0000}{") * z(C)) * "})-(\textcolor{#000099}{") * z(B)) * "})(\textcolor{#CC0000}{") * x(C)) * "})] \cr\text{ }+\hat{k}[(\textcolor{#000099}{") * y(B)) * "})(\textcolor{#CC0000}{") * z(C)) * "})-(\textcolor{#000099}{") * z(B)) * "})(\textcolor{#CC0000}{") * y(C)) * "})] \cr=(") * x(crossProduct)) * ",") * y(crossProduct)) * ",") * z(crossProduct)) * ")")) → text3