[Tex/LaTex] How to draw a coordinate system without grid or scale

tikz-pgf

enter image description here

I hope to draw coordinate system for three-dimensional space that has a line through the origin as the above picture using TikZ as similar as possible. But the examples of graphs I found have grids or scales. Is there a useful code to draw this?

\documentclass{article}   
\usepackage{tikz}  
\begin{document}  
\begin{tikzpicture}  

%\psset{algebraic,arrows=<->} ? failed... what should I put?  

\end{tikzpicture}  
\end{document}  

[still it's hard to place a desired angle and length….]

enter image description here

\documentclass{article}   
\usepackage{tikz}  
\begin{document}  
\begin{tikzpicture}[
   axisline/.style={very thick,-stealth},
   rotate around y=10,
   ]
\draw [axisline] (-3,0,0) -- (3,0,0) node[right]{$x_2$};
\draw [axisline] (0,-3,0) -- (0,3,0) node[left]{$x_3$};

\draw [axisline, cyan] (0,0,1) -- (1,1,2) node[right]{$x_k$};
\draw [axisline] (0,0,1) -- (1,1,2) node[right]{$v$};


 \end{tikzpicture}  
 \end{document}

[made a similar picture]

enter image description here

\documentclass[tikz,border=2mm]{standalone}   
\usepackage{tikz}  
\begin{document}  
\begin{tikzpicture}[axisline/.style={very thick, -stealth}]  

\draw[axisline] (-3,1,0)--(3,-1,0) node[right]{$x_2$};
\draw[axisline] (0,-2.5,0)--(0,3,0) node[above]{$x_3$};
\draw[axisline] (0,0,-3)--(0,0,4) node[below left]{$x_1$};
\draw[cyan] (1, 3, 0)--(-1, -3, 0);
\draw[axisline] (0,0,0)--(0.4,1.2,0) node[right]{$v$};

\end{tikzpicture}  
\end{document}

Best Answer

TikZ allows you to specify coordinates in three dimensions, so just draw some lines.

\documentclass{article}   
\usepackage{tikz}  
\begin{document}  
\begin{tikzpicture}[
  axisline/.style={very thick,-stealth},
  rotate around y=10,
]
\draw [axisline] (-3,0,0) -- (3,0,0) node[right]{$x_1$};
\draw [axisline] (0,-3,0) -- (0,3,0) node[right]{$x_2$};
\draw [axisline] (0,0,-3) -- (0,0,3) node[right]{$x_3$};

\draw [cyan] (-2,-2,-2) -- (2,2,2);
\draw [thick,-latex] (0,0,0) -- (1,1,1) node[right]{$\mathbf{v}$};
\end{tikzpicture}  
\end{document}

enter image description here