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+%
+% drehung.tex
+%
+% (c) 2021 Prof Dr Andreas Müller, OST Ostschweizer Fachhochschule
+%
+\documentclass[tikz]{standalone}
+\usepackage{times}
+\usepackage{amsmath}
+\usepackage{txfonts}
+\usepackage[utf8]{inputenc}
+\usepackage{graphics}
+\usetikzlibrary{arrows,intersections,math}
+\usepackage{ifthen}
+\begin{document}
+
+\definecolor{darkgreen}{rgb}{0,0.6,0}
+\definecolor{darkred}{rgb}{0.6,0,0}
+
+\newboolean{showgrid}
+\setboolean{showgrid}{false}
+\def\breite{7}
+\def\hoehe{6}
+
+\begin{tikzpicture}[>=latex,thick]
+
+% Povray Bild
+\node at (0,0) {\includegraphics[width=13cm]{drehung.jpg}};
+
+% Gitter
+\ifthenelse{\boolean{showgrid}}{
+\draw[step=0.1,line width=0.1pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw[step=0.5,line width=0.4pt] (-\breite,-\hoehe) grid (\breite, \hoehe);
+\draw (-\breite,-\hoehe) grid (\breite, \hoehe);
+\fill (0,0) circle[radius=0.05];
+}{}
+
+\node at (6.1,-3.3) {$a_1$};
+\node at (-2.0,5.7) {$a_2$};
+\node at (-5.7,-4.9) {$a_3$};
+
+\node[color=white] at (-1.9,4.4) {$\boldsymbol{v}$};
+\node[color=white] at (4.5,-2.7) {$\boldsymbol{v}''$};
+
+\node[color=darkgreen] at (-3.3,4.4) {$\boldsymbol{v}_{\perp}$};
+\node[color=darkgreen] at (4.2,-4.3) {$\boldsymbol{v}''_{\perp}$};
+
+\node[color=blue] at (-3.7,1.5) {$\boldsymbol{v}_{\|}$};
+\node[color=blue] at (1.9,-4.7) {$\boldsymbol{v}''_{\|}$};
+
+\node[color=darkred] at (-1.6,-4.2) {$2\alpha=120^\circ$};
+\node[color=darkred] at (-4.9,-0.6) {$\boldsymbol{q}$};
+
+\end{tikzpicture}
+
+\end{document}
+