绘制一些简单的正交投影

Question

我是 TikZ 的新手，我想展示一个矢量是可以分解为

我怎样才能告诉 TikZ 绘制一条与是_到​X和一个向量ε正交于X，从原点开始？这是代码，但缺少投影。

\documentclass[12pt,a4paper]{article}

\usepackage{tikz}
\usetikzlibrary{calc} 
\usetikzlibrary{positioning,arrows.meta}
\begin{document}

\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
  extended line/.style={shorten >=-#1,shorten <=-#1},
  extended line/.default=1cm]

\draw[thick,->] (-4.5,0) -- (4.5,0);
\draw[thick,->] (0,0) -- (0,4.5);

\coordinate (A) at (0,0);
\coordinate (B) at (-4,3);

\draw [extended line=0.5cm, <->] (A) -- (B) 
node[pos=0.8,left=1em, font=\small]{$X$};     
\draw [ ->] (0,0) -- (-2.6, 4.3) node[anchor=north east,font=\small] {$y$};

\end{tikzpicture}
\end{document}

Answer 1

可以使用 来将坐标投影到和(yn)之间的线上，如(A)(B)($(A)!(yn)!(B)$)Marian G. 链接的帖子为了得到图像，你可能想要简单地（意味着没有交叉点、明确的角度等）做

\documentclass[12pt,a4paper]{article}
\usepackage{tikz}
\usetikzlibrary{calc,positioning}
\begin{document}
\begin{tikzpicture}[dot/.style={circle,inner sep=1pt,fill,label={#1},name=#1},
  extended line/.style={shorten >=-#1,shorten <=-#1},
  extended line/.default=1cm]
 \draw[thick,-stealth] (-4.5,0) -- (4.5,0);
 \draw[thick,-stealth] (0,0) -- (0,4.5);
 \coordinate (A) at (0,0);
 \coordinate (B) at (-4,3);
 \draw [extended line=0.5cm, stealth-stealth] (A) -- (B) node[pos=1.15,font=\small]{$X$};     
 \draw [ -stealth] (0,0) -- (-2.6, 4.3) coordinate (yn) node[right]{$y$}; 
 \draw[dashed] (yn) --  node[midway,above left]{$\varepsilon$} ($(A)!(yn)!(B)$) node[below left]{$y_p$};
\end{tikzpicture}
\end{document}

Answer 2

作为起点：

\documentclass[12pt,tikz, margin=3mm]{standalone}
\usetikzlibrary{arrows.meta,
                calc,
                intersections,
                quotes}

\begin{document}
    \begin{tikzpicture}[
          lbl/.style = {inner sep=2pt, font=\footnotesize, sloped},
   every path/.style = {-Straight Barb},
extended line/.style = {shorten >=-#1,shorten <=-#1},
extended line/.default = 1cm
                    ]
\draw[semithick] (-4.5,0) -- (4.5,0);
\draw[semithick] (0,-0.5) -- (0,4.5);
%
\coordinate (A) at (0,0);
\coordinate (B) at (-3.2,1.6);
\coordinate (C) at (-2.6,4.3);
%
\path[name path=X] (A) -- (C);                  % <---
\path[name path=P] (B) -- ($(B)!1!90:(A)$);     % <---
\draw[name intersections={of=P and X, by={p}},  % <---
      dashed,->]                                % <---
    (B) -- node[lbl,above] {$y_q$} (p);         % <---
\draw[thick] (A) -- node[lbl,above] {$y$}
             (p)  node[above] {$Y$};
\draw[dashed] (A) -- node[lbl,below] {$y_d$} (B);
\end{tikzpicture}
\end{document}