解析幾何圖解

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\documentclass[UTF8,a1paper,landscape]{ctexart}\usepackage{tikz}\usepackage{amsmath}\usepackage{amssymb}\usepackage{geometry}\geometry{top=5cm,bottom=5cm,left=5cm,right=5cm}\usepackage{fancyhdr}\pagestyle{fancy}\begin{document}    \title{\Huge 解析幾何圖解}    \author{dengchaohai}    \maketitle    \newpage    \begin{center}        \begin{tikzpicture}        [r/.style={rectangle,black,draw,align=left,rounded corners=.8ex}]        \node(1)at (-20,0)[r]{1標架$\begin{cases}            \text{一維} & \text{數軸}\            \text{二維} & \begin{cases}            \text{直座標系}\            \text{極座標系}            \end{cases}\            \text{三維} & \begin{cases}            \text{直座標系}\            \text{極座標系} & \begin{cases}            \text{球座標系}\            \text{柱座標系}            \end{cases}            \end{cases}            \end{cases}$            };        \node(2)at (0,10)[r]{2標量$$};        \node(3)at (0,-10)[r]{3向量$$};        \node(4)at (20,5)[r]{4座標$P(x,y,z)$\begin{tabular}{|c|c|c|c|c|}            \hline             & 向量 &  & 二向量 & 三向量\tabularnewline            \hline             加法 & $(x_{1},y_{1},z_{1})+(x_{2},y_{2},z_{2})=(x_{1}+x_{2},y_{1}+y_{2},z_{1}+z_{2})$ & 點乘 & $(x_{1},y_{1},z_{1})\cdot(x_{2},y_{2},z_{2})=x_{1}x_{2}+y_{1}y_{2}+z_{1}z_{2}$ & $(x_{1},y_{1},z_{1})\times(x_{2},y_{2},z_{2})\cdot(x_{3},y_{3},z_{3})=\begin{vmatrix}            x_{1} & y_{1} & z_{1}\            x_{2} & y_{2} & z_{2}\            x_{3} & y_{3} & z_{3}            \end{vmatrix}$ \tabularnewline            \hline             數乘 & $\lambda(x,y,z)=(\lambda x,\lambda y,\lambda z)$ & 叉乘 & $(x_{1},y_{1},z_{1})\times(x_{2},y_{2},z_{2})=\begin{vmatrix}i & j & k\            x_{1} & y_{1} & z_{1}\            x_{2} & y_{2} & z_{2}            \end{vmatrix}$ & \tabularnewline            \hline             \end{tabular}};        \node(5)at (20,-5)[r]{5向徑$\vec{r}\{X,Y,Z\}$\begin{tabular}{|c|c|c|c|c|}            \hline             & 向量 &  & 二向量 & 三向量\tabularnewline            \hline             加法 & $\vec{a}+\vec{b}$ & 點乘 & $\vec{a}\cdot\vec{b}$ & $\vec{a}\times\vec{b}\cdot\vec{c}$\tabularnewline            \hline             數乘 & $\lambda\vec{a}$ & 叉乘 & $\vec{a}\times\vec{b}$ & $\vec{a}\times\vec{b}\times\vec{c}$\tabularnewline            \hline             \end{tabular}};        \node(6)at (10,0)[r]{6軌跡$\begin{cases}\text{點}\\\text{線}\\\text{面}\\\text{體}\end{cases}$};        \node(7)at (30,0)[r]{7方程$\begin{cases}\text{座標式}\\\text{向徑式}\end{cases}$};                \draw(1)--(2) (1)--(3) (4)--(6) (5)--(6) (6)--(7) (-10,5)--(4) (-10,-5)--(5);        \end{tikzpicture}    \end{center}    \newpage    \begin{center}        \end{center}\end{document}

解析幾何圖解