平行四边形的面积 by Peter Johnston

几何画板及绘图内容加载中，请稍等……

2016-05-19 06:47

这个范例演示了如何通过向量和解析几何计算平行四边形的面积。核心数学概念包括向量的叉积和解析几何中的多边形。通过使用GeoGebra命令如Vector、Polygon和crossProduct，可以直观地展示平行四边形的构造过程。适合初中及以上学生学习几何和向量的相关知识。

GeoGebra 命令及参数

Vector(A, B) → u
Vector(A, C) → v
TableText({{LaTeX["\hat{i}"], LaTeX["\hat{j}"], LaTeX["\hat{k}"]}, {LaTeX[(("\textcolor{#000099}{" * x(u)) * "}")], LaTeX[(("\textcolor{#000099}{" * y(u)) * "}")], LaTeX[(("\textcolor{#000099}{" * z(u)) * "}")]}, {LaTeX[(("\textcolor{#CC0000}{" * x(v)) * "}")], LaTeX[(("\textcolor{#CC0000}{" * y(v)) * "}")], LaTeX[(("\textcolor{#CC0000}{" * z(v)) * "}")]}}, "||c") → text2
Polygon(A, B, D, C) → poly1, f, g, h, i
LaTeX($1) → text5
LaTeX((((((((((((((((((((((((((((((((("\textcolor{#000099}{\vec{AB}}\times\textcolor{#CC0000}{\vec{AC}}\cr=\text{ }" * text2) * " \cr=\hat{i}[(\textcolor{#000099}{") * y(u)) * "})(\textcolor{#CC0000}{") * z(v)) * "})-(\textcolor{#000099}{") * z(u)) * "})(\textcolor{#CC0000}{") * y(v)) * "})] \cr\text{ }-\hat{j}[(\textcolor{#000099}{") * x(u)) * "})(\textcolor{#CC0000}{") * z(v)) * "})-(\textcolor{#000099}{") * z(u)) * "})(\textcolor{#CC0000}{") * x(v)) * "})] \cr\text{ }+\hat{k}[(\textcolor{#000099}{") * x(u)) * "})(\textcolor{#CC0000}{") * y(v)) * "})-(\textcolor{#000099}{") * y(u)) * "})(\textcolor{#CC0000}{") * x(v)) * "})] \cr=(") * x(crossProduct)) * ",") * y(crossProduct)) * ",") * z(crossProduct)) * ")")) → text3