解析几何图解

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\begin{document}
    \title{\Huge 解析几何图解}
    \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标架$\begin{cases}
            \text{一维} & \text{数轴}\\
            \text{二维} & \begin{cases}
            \text{直坐标系}\\
            \text{极坐标系}
            \end{cases}\\
            \text{三维} & \begin{cases}
            \text{直坐标系}\\
            \text{极坐标系} & \begin{cases}
            \text{球坐标系}\\
            \text{柱坐标系}
            \end{cases}
            \end{cases}
            \end{cases}$
            };
        \node(2)at (0,10)[r]{2标量$$};
        \node(3)at (0,-10)[r]{3向量$$};
        \node(4)at (20,5)[r]{4坐标$P(x,y,z)$\begin{tabular}{|c|c|c|c|c|}
            \hline 
            & 向量 &  & 二向量 & 三向量\tabularnewline
            \hline 
            加法 & $(x_{1},y_{1},z_{1})+(x_{2},y_{2},z_{2})=(x_{1}+x_{2},y_{1}+y_{2},z_{1}+z_{2})$ & 点乘 & $(x_{1},y_{1},z_{1})\cdot(x_{2},y_{2},z_{2})=x_{1}x_{2}+y_{1}y_{2}+z_{1}z_{2}$ & $(x_{1},y_{1},z_{1})\times(x_{2},y_{2},z_{2})\cdot(x_{3},y_{3},z_{3})=\begin{vmatrix}
            x_{1} & y_{1} & z_{1}\\
            x_{2} & y_{2} & z_{2}\\
            x_{3} & y_{3} & z_{3}
            \end{vmatrix}$ \tabularnewline
            \hline 
            数乘 & $\lambda(x,y,z)=(\lambda x,\lambda y,\lambda z)$ & 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向径$\vec{r}\{X,Y,Z\}$\begin{tabular}{|c|c|c|c|c|}
            \hline 
            & 向量 &  & 二向量 & 三向量\tabularnewline
            \hline 
            加法 & $\vec{a}+\vec{b}$ & 点乘 & $\vec{a}\cdot\vec{b}$ & $\vec{a}\times\vec{b}\cdot\vec{c}$\tabularnewline
            \hline 
            数乘 & $\lambda\vec{a}$ & 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轨迹$\begin{cases}\text{点}\\\text{线}\\\text{面}\\\text{体}\end{cases}$};
        \node(7)at (30,0)[r]{7方程$\begin{cases}\text{坐标式}\\\text{向径式}\end{cases}$};
        
        \draw(1)--(2) (1)--(3) (4)--(6) (5)--(6) (6)--(7) (-10,5)--(4) (-10,-5)--(5);
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    \end{center}
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\end{document}