\documentclass[12pt,a4paper]{article}
\usepackage{pstricks}
\usepackage{pst-3dplot}

\begin{document}

\begin{pspicture}(-6,-6)(6,6)
\psset{unit=7.5cm,hiddenLine=true,drawCoor=true}
\def\oA{%
  \pstThreeDLine[linecolor=blue,linewidth=3pt,%
    SphericalCoor=true,arrows=c-> ](0,0,0)(1,60,70)%
}
\def\oB{%
  \pstThreeDLine[linecolor=red,linewidth=3pt,%
    SphericalCoor=true,arrows=c->](0,0,0)(1,10,50)%
}
\def\oAB{%
  \pstThreeDEllipse[beginAngle=90,endAngle=122,fillcolor=green,%
    SphericalCoor=true](0,0,0)(1,140,40)(1,10,50)%
}
\pstThreeDCoor[drawing=true, linewidth=1pt,linecolor=black,%
  xMin=0,xMax=1.1, yMin=0,yMax=1.1, zMin=0,zMax=1.1]
\pstThreeDEllipse[beginAngle=0, endAngle=90,linestyle=dotted]%
  (0,0,0)(-1,0,0)(0,1,0)
\pstThreeDEllipse[beginAngle=0, endAngle=90,linestyle=dotted]%
  (0,0,0)(-1,0,0)(0,0,1)
\pstThreeDEllipse[beginAngle=180, endAngle=90,linestyle=dotted]%
  (0,0,0)(0,0,1)(0,1,0)

\psset{SphericalCoor=true}
\pstThreeDDot[dotstyle=none](1,10,50)
\pstThreeDDot[dotstyle=none](1,60,70)
\pscustom[fillstyle=crosshatch,hatchcolor=yellow,%
  linestyle=none]{\oA\oB\oAB}
\oA \oB \oAB
\pstThreeDPut[origin=lb](1,60,70){\Large $\vec\Omega_1$}
\pstThreeDPut[origin=rb](1,10,50){\Large $\vec\Omega_2 \,$}
\pstThreeDPut[origin=lb](1,10,65){\Large $\gamma_{12}$}

\end{pspicture}
\end{document}
