向量问题（tikz）

Question

我必须绘制这些矢量，带有网格和网格（如图所示）。我在网上搜索过，但无法解决我的问题。你能帮助我吗？

\documentclass[a4paper]{minimal}

\usepackage[centering,margin=0.5cm]{geometry}
\usepackage{tikz}
\pagestyle{empty}

\begin{document}
\noindent\begin{tikzpicture}[color=gray]
%\draw[line width=0.10pt, step=1.0mm] (0,0) grid +(20cm,28cm);
%\draw[line width=0.25pt, step=5.0mm] (0,0) grid +(20cm,28cm);
\draw[line width=0.05pt, step=0.5cm] (0,0) grid +(10cm,5cm);
\end{tikzpicture}
\end{document}

我想画出如图所示的角。并且想在角内添加颜色。

Answer 1

从您的 MWE 到下面的图片只是一小步：

\documentclass[a4paper]{minimal}

\usepackage[centering,margin=2cm]{geometry}
\usepackage{tikz}
\pagestyle{empty}

\begin{document}
\noindent\begin{tikzpicture}[> = stealth]
\draw[gray,step=1cm] (0,0) grid +(9cm,6cm);
    \draw[ultra thick,red, ->]  (1,4) -- node[above] {$\vec{a}$} +(2,0);
    \draw[ultra thick,blue,->]  (1,3) -- node[below left] {$\vec{b}$} +(1,-2);
%
    \draw[ultra thick,red, ->]  (4,4) -- node[above] {$\vec{a}$} +(1,0);
    \draw[ultra thick,blue,->]  (4,4) -- node[below left] {$\vec{b}$} +(1,-2);
    %
    \draw[ultra thick,blue,|-|] (6,1) -- node[below] {$u$} +(1,0);
\end{tikzpicture}
\end{document}