\documentclass[a4]{article}

\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}
\usepackage{amsmath,amsfonts,amssymb}
\usepackage{graphicx}
\usepackage[usenames,dvipsnames]{xcolor}
%\usepackage{tikz}

\usepackage{pgfplots}
\usepackage{tikz,animate}
\usepackage{pgfplots}
\usetikzlibrary{shapes.arrows}
\usetikzlibrary{arrows.meta}

\usetikzlibrary{calc,patterns,angles,quotes}
\begin{document}
\pagestyle{empty}


\begin{tikzpicture}[>={Stealth[scale=1]}]



\begin{scope}[rotate=60]
\draw[thick,fill=blue,opacity=0.250] (0,0) ellipse (2 cm and 1 cm);
\draw[thick] (0,0) ellipse (2 cm and 1 cm);
\draw[-, thick](-2,0) -- (2,0);
\draw[-,thick](0,-1) -- (0,1);
\end{scope}

%\draw[-, thick](-1,-1.73) -- (1, 1.73);
\draw (-0.7,-0.7) node [text=black]{{ $a$}};
%\draw[-, thick](-0.87,0.5) -- (0.87,-0.5);
\draw (-0.7, 0.1) node [text=black]{{ $b$}};

  \coordinate (origo) at (0,0); 
  \coordinate (zaxis) at (0,4); 
  \coordinate (ellipseorientation) at (2,3.46); 
  
  
 \pic [draw, ->, "$\theta_1$", angle eccentricity=0.7, angle radius =1.25cm] {angle = ellipseorientation--origo--zaxis};

\draw[->,  thick] (0,0) -- (4.5, 0);
\draw (4.0,-0.5) node [text=black]{{ $x$}};

\draw[->,  thick] (0,0) -- (0, 3.5);
\draw (-0.5,4.0) node [text=black]{{  $z$}};

\begin{scope}[shift={(2.5,1.35)},rotate=130]
\draw[thick,fill=blue,opacity=0.25] (0,0) ellipse (2 cm and 1 cm);
\draw[ thick] (0,0) ellipse (2 cm and 1 cm);
\draw[-, thick](-2,0) -- (2,0);
\draw[-,thick](0,-1) -- (0,1);
\end{scope}
\draw[-, thick,  dashed] (2.5,1.35) -- (2.5, 3.85);
  \coordinate (eorigo) at (2.5,1.35); 
 \coordinate (ezaxis) at (2.5,3.85); 
  \coordinate (eellipseorientation) at (3.6,0); 
 
 \pic [draw, ->, "$\theta_2$", angle eccentricity=0.75, angle radius =0.8cm] {angle = eellipseorientation--eorigo--ezaxis};


\draw[->, very thick, blue] (0,0) -- (2.5,1.35);


\draw (1.3, 0.95) node [scale=0.7, text=blue, rotate=30]{{  $d_c(\mathbf{e}_{12}, \mathbf{u}_1,\mathbf{u}_2; \epsilon) \mathbf{e}_{12}$}};
%\draw (0.8, 0.65) node [scale=1.0, text=blue, rotate=30]{{  $d_c\mathbf{e}_{12}$}};
%\draw (2.0, -1.55) node [scale=1.0, text=blue]{{  $d_c = d_c(\mathbf{e}_{12}, \mathbf{u}_1,\mathbf{u}_2; \epsilon) $}};

%\draw (1.0, 0.3) node [scale= 0.6, text=blue, rotate=30]{{$d_c(\mathbf{e}_{12}, \mathbf{u}_1,\mathbf{u}_2) \mathbf{e}_{12}$}};
\end{tikzpicture}


\end{document}