\begin{tikzpicture}[>=latex]
   \tkzDefPoint(1,4){a}
   \tkzDefPoint(3,2){b}
   \tkzDefPoint(1,1){c}
   \tkzDrawSegment[->,red](a,b)
   \tkzGetPointCoord(c){c}
   \draw[color=blue,->](a) -- ([shift=(b)]\cx,\cy) ;
   \draw[color=purple,->](b) -- ([shift=(b)]\cx,\cy) ;
   \tkzDrawSegment[->,blue](a,c)
   \tkzDrawSegment[->,purple](b,c)
\end{tikzpicture}
