三维坐标系统下作垂线，只找到2维坐标系统下作垂线，简单复制到3维坐标，貌似有问题，是我数学太菜了吗？

要想实现三维绘制垂线，需要自己做向量计算：

\documentclass[tikz,border=6pt]{standalone}
\usepackage{tikz-3dplot}
\usetikzlibrary{calc}
\begin{document}
\tdplotsetmaincoords{60}{110}
\begin{tikzpicture}[tdplot_main_coords]
  % Axes
  \draw[thick, ->] (0,0,0) -- (4,0,0) node[right] {$x$};
  \draw[thick, ->] (0,0,0) -- (0,3,0) node[right] {$y$};
  \draw[thick, ->] (0,0,0) -- (0,0,2) node[above] {$z$};

  % Points
  \coordinate (A) at (0,1,0);
  \coordinate (B) at (3,2,0);
  \coordinate (C) at (2.5,0,1);

  % Labels
  \path node[above] at (A) {$A$} node[above] at (B) {$B$} node[above] at (C) {$C$};
  \fill[red] (A) circle (1pt) (B) circle (1pt) (C) circle (1pt);

  % Compute projection D
  \pgfmathsetmacro{\ABx}{3 - 0} % Bx - Ax
  \pgfmathsetmacro{\ABy}{2 - 1} % By - Ay
  \pgfmathsetmacro{\ABz}{0 - 0} % Bz - Az
  \pgfmathsetmacro{\ACx}{2.5 - 0} % Cx - Ax
  \pgfmathsetmacro{\ACy}{0 - 1} % Cy - Ay
  \pgfmathsetmacro{\ACz}{1 - 0} % Cz - Az

  % Dot products
  \pgfmathsetmacro{\ABdotAB}{\ABx*\ABx + \ABy*\ABy + \ABz*\ABz}
  \pgfmathsetmacro{\ACdotAB}{\ACx*\ABx + \ACy*\ABy + \ACz*\ABz}

  % Parameter t for projection
  \pgfmathsetmacro{\t}{\ACdotAB / \ABdotAB}

  % Coordinates of D
  \pgfmathsetmacro{\Dx}{0 + \t * \ABx}
  \pgfmathsetmacro{\Dy}{1 + \t * \ABy}
  \pgfmathsetmacro{\Dz}{0 + \t * \ABz}

  % Draw projection
  \coordinate (D) at (\Dx,\Dy,\Dz);
  \fill[blue] (D) circle (1pt) node[right] at (D) {$D$};
  \draw[cyan] (A) -- (B) (C) -- (D);
\end{tikzpicture}
\end{document}

核心思路是利用向量的投影和加减运算。

另外，下次提问请务必给可以编译测试的例子。