TiKz. Angle between two vectors and a projection

Question

I'm having trouble to draw something with TiKz. What I want to draw I think is simple:

SIM is a vector in the YZ-plane with a Beta = 38º, source is just a random vector with positive x and y components and negative z. Theta is the angle between SIM and source vectors and Phi is the angle formed by the source projection in the XZ-plane with the X-axis.

Thanks a lot in advance

Answer 1

Here is a tikz-3dplot approach. The arcs are drawn using:

% define three points
\tdplotdefinepoints(vx, vy, vz)(ax, ay, az)(bx, by, bz)
% draw arc using the three points and a radius
\tdplotdrawpolytopearc[draw style]{r}{label options}{label}

The viewpoint can be modified using:

\tdplotsetmaincoords{rotation around x}{rotation around z}

The x-axis and z-axis can be exchanged using:

\let\raarotold\raarot \let\rbarotold\rbarot
\let\rabrotold\rabrot \let\rbbrotold\rbbrot
\let\racrotold\racrot \let\rbcrotold\rbcrot

\let\raarot\racrotold \let\rbarot\rbcrotold
\let\rabrot\rabrotold \let\rbbrot\rbbrotold
\let\racrot\raarotold \let\rbcrot\rbarotold

Note: The -z-axis in the following picture is actually the z-axis. I have just changed the label.

See Symbol 1's answer here for details about coordinate system customization.

\documentclass[tikz]{standalone}
\usepackage{tikz-3dplot}

\begin{document}
\tdplotsetmaincoords{60}{120}

% customized coordinate system
\let\raarotold\raarot \let\rbarotold\rbarot
\let\rabrotold\rabrot \let\rbbrotold\rbbrot
\let\racrotold\racrot \let\rbcrotold\rbcrot

\let\raarot\racrotold \let\rbarot\rbcrotold
\let\rabrot\rabrotold \let\rbbrot\rbbrotold
\let\racrot\raarotold \let\rbcrot\rbarotold

\begin{tikzpicture}[tdplot_main_coords]

  % axes
  \draw[thick,->] (0,0,0) -- ( 7,0,0) node[anchor=south]{$x$};
  \draw[thick,->] (0,0,0) -- ( 0,7,0) node[anchor=west]{$y$};
  \draw[thick,->] (0,0,0) -- ( 0,0,7) node[anchor=north east]{$-z$};  
  \draw[thick]    (0,0,0) -- ( 0,-2,0);
  \draw[thick,->] (0,0,0) -- ( 0,0,-7) node[anchor=south west]{$z$};

  % vector 1
  \pgfmathsetmacro{\ax}{5}
  \pgfmathsetmacro{\ay}{5}
  \pgfmathsetmacro{\az}{2}
  \draw[very thick,->,red] (0,0,0) -- (\ax,\ay,\az) node[anchor=west]{source};

   % vector 2
  \pgfmathsetmacro{\bx}{0}
  \pgfmathsetmacro{\by}{3}
  \pgfmathsetmacro{\bz}{4}
  \draw[very thick,->,blue] (0,0,0) -- (\bx,\by,\bz) node[anchor=north]{sim};

   % vector 3 (projection)
  \pgfmathsetmacro{\cx}{\ax*1.2}
  \pgfmathsetmacro{\cy}{0}
  \pgfmathsetmacro{\cz}{\az*1.2}
  \draw[very thick,green] (0,0,0) -- (\cx,\cy,\cz);

   % dashed lines
%  \draw[dashed,gray] (\ax,\ay,\az) -- (\ax,\ay,0);
  \draw[dashed,gray] (\ax,\ay,\az) -- (\ax,0,\az);
  \draw[dashed,gray] (\ax,\ay,\az) -- (0,\ay,\az);
%  \draw[dashed,gray] (\ax,0,0) -- (\ax,\ay,0) -- (0,\ay,0);
  \draw[dashed,gray] (\ax,0,0) -- (\ax,0,\az) -- (0,0,\az);
  \draw[dashed,gray] (0,0,\az) -- (0,\ay,\az) -- (0,\ay,0);

  % arcs
  \tdplotdefinepoints(0,0,0)(\ax,\ay,\az)(\bx,\by,\bz)
  \tdplotdrawpolytopearc[<->]{2}{anchor=north west}{$\theta$}
  \tdplotdefinepoints(0,0,0)(0,0,1)(\bx,\by,\bz)
  \tdplotdrawpolytopearc[<->]{3}{anchor=north}{$\beta$}
  \tdplotdefinepoints(0,0,0)(1,0,0)(\cx,\cy,\cz)
  \tdplotdrawpolytopearc[<->]{4}{anchor=north}{$\phi$}

\end{tikzpicture}
\end{document}

Answer 2

This should do the job. Feel free to adapt the styles.

I suggest you define the coordinates of source individually, so that the projection onto the two planes and the axes can be done more easily. (The let...in syntax is not an option, because it does not work with 3d coordinates.)

\documentclass[border=5pt]{standalone}

\usepackage{tikz}
\usetikzlibrary{3d,angles,quotes,calc}

\begin{document}
\begin{tikzpicture}[axes/.style={thick,->},
    z={(.5,{.5*sqrt(3)})},
    y={({.5*sqrt(3)},-.5)},
    x={(0,-.5,{.5*sqrt(3)})}]

   \draw[axes] (0,0,0) coordinate (O) -- (6,0,0) coordinate (X) node [right]{$x$};
   \draw[axes] (O) -- (0,6,0) node [above]{$y$};
   \draw[axes,<->] (0,0,-6) coordinate (Z') node [below left] {$-z$}
        -- (0,0,6) coordinate (Z) node [above right] {$z$} ;


   \pgfmathsetmacro{\sourcex}{5}
   \pgfmathsetmacro{\sourcey}{5}
   \pgfmathsetmacro{\sourcez}{-2}
   \coordinate (Source) at (\sourcex,\sourcey,\sourcez);
   \coordinate (Source on xz) at (\sourcex,0,\sourcez);
   \coordinate (Source on yz) at (0,5,-2);
   \coordinate (Source on xz) at (5,0,-2);
   \coordinate (Source on x axis) at (5,0,0);
   \coordinate (Source on y axis) at (0,5,0);
   \coordinate (Source on z axis) at (0,0,-2);

   \begin{scope}[canvas is yz plane at x=0]
      \coordinate (SIM) at (-38:4);
   \end{scope}

   \draw[dotted] (\sourcex,0,\sourcez) -- (Source) -- (0,\sourcey,\sourcez);
   \draw[dotted] (\sourcex,0,0) -- (Source on xz) -- (0,0,\sourcez);
   \draw[dotted] (0,\sourcey,0) -- (0,\sourcey,\sourcez) -- (0,0,\sourcez);

   \pic [draw,angle radius=.6cm,angle eccentricity=1.4,"$\phi$"] 
        {angle = X--O--Source on xz};
   \pic [draw,angle radius=.5cm,angle eccentricity=1.5,"$\beta$"] 
        {angle = Z'--O--SIM};
   \pic [draw,fill=white,angle radius=.7cm,angle eccentricity=.6,"$\theta$"] 
        {angle = SIM--O--Source};

   \draw (O) -- (Source on xz);
   \draw[->] (0,0,0) -- (Source) node[above right] {Source};
   \draw[->] (0,0) --  (SIM) node[below] {Sim};
\end{tikzpicture}
\end{document}

Answer 3

You can draw this shape in geogebra, and export it to tikz, easily. This is a sample:

\documentclass[10pt]{article}
\usepackage{pgf,tikz}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\newcommand{\degre}{\ensuremath{^\circ}}
\begin{document}
\definecolor{qqwuqq}{rgb}{0.,0.39215686274509803,0.}
\definecolor{qqqqff}{rgb}{0.,0.,1.}
\definecolor{cqcqcq}{rgb}{0.7529411764705882,0.7529411764705882,0.7529411764705882}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\draw [color=cqcqcq,dash pattern=on 3pt off 3pt, xstep=1.0cm,ystep=1.0cm] (-4.3,-2.66) grid (7.3,6.3);
\clip(-4.3,-2.66) rectangle (7.3,6.3);
\draw [shift={(1.,0.)},color=qqwuqq,fill=qqwuqq,fill opacity=0.1] (0,0) -- (-26.56505117707799:0.6) arc (-26.56505117707799:90.:0.6) -- cycle;
\draw (1.,3.)-- (1.,0.);
\draw (1.,0.)-- (5.,-2.);
\begin{scriptsize}
\draw [fill=qqqqff] (1.,3.) circle (1.5pt);
\draw[color=qqqqff] (1.14,3.28) node {$A$};
\draw [fill=qqqqff] (1.,0.) circle (1.5pt);
\draw[color=qqqqff] (1.14,0.28) node {$B$};
\draw[color=black] (0.74,1.68) node {$a$};
\draw [fill=qqqqff] (5.,-2.) circle (1.5pt);
\draw[color=qqqqff] (5.14,-1.72) node {$C$};
\draw[color=qqwuqq] (2.64,0.44) node {$\alpha = 116.57\textrm{\degre}$};
\draw[color=black] (2.9,-1.12) node {$b$};
\end{scriptsize}
\end{tikzpicture}
\end{document}