\documentclass[]{article}
\usepackage{pstricks}
\usepackage{pst-3dplot}
\pagestyle{empty}
\parindent=0pt

\begin{document}

\begin{center}
\begin{pspicture}(-4.8,-1.5)(4.8,3.5)
\psset{unit=5cm,drawCoor,beginAngle=90,endAngle=180,linestyle=dotted}
\def\oA{\pstThreeDLine[linecolor=blue,linewidth=3pt,arrows=c-> ](0,0,0)(1,60,70)}
\def\oB{\pstThreeDLine[linecolor=red,linewidth=3pt,arrows=c->](0,0,0)(1,10,50)}
\def\oAB{\pstThreeDEllipse[beginAngle=58,endAngle=90](0,0,0)(1,140,40)(1,10,50)}
\pstThreeDCoor[drawing=true, linewidth=1pt,linecolor=black,linestyle=solid,%
  xMin=0,xMax=1.1, yMin=0,yMax=1.1, zMin=0,zMax=1.1]
\pstThreeDEllipse(0,0,0)(-1,0,0)(0,1,0)
\pstThreeDEllipse(0,0,0)(-1,0,0)(0,0,1)
\pstThreeDEllipse[beginAngle=0,endAngle=90](0,0,0)(0,0,1)(0,1,0)
\psset{SphericalCoor,linestyle=solid}
\pstThreeDDot[dotstyle=none](1,10,50)
\pstThreeDDot[dotstyle=none](1,60,70)
\pscustom[fillstyle=crosshatch,hatchcolor=yellow,linestyle=none]{\oB\oAB\oA}
\oA \oB \oAB
\pstThreeDPut[origin=lb](1,60,70){$\vec\Omega_1$}
\pstThreeDPut[origin=rb](1,10,50){$\vec\Omega_2 \,$}
\pstThreeDPut[origin=lb](1,10,65){$\gamma_{12}$}
\end{pspicture}
\end{center}

\end{document}

