d
\(\begin{array}{l}
\,\,\,At\,time\,t = 0,\,the\,position\,vector\,of\\
the\,particle\,is\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{\bar r}_1} = 2\hat i + 3\hat j\\
At\,time\,t = 5\,s,\,the\,position\,vector\,of\\
the\,particle\,is\,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,{{\bar r}_2} = 13\hat i + 14\hat j\\
Displacement\,from\,\,\,{{\bar r}_1}\,to\,\,{{\bar r}_2}\,is
\end{array}\)

\(\begin{array}{l}
Displacement\,from\,\,\,{{\bar r}_1}\,to\,\,{{\bar r}_2}\,is\\
\Delta \bar r = {{\bar r}_2} - {{\bar r}_1} = \left( {13\hat i + 14\hat j} \right) - \left( {2\hat i + 3\hat j} \right)\\
 = 11\hat i + 11\hat j\\
\therefore \,\,\,Average\,velocity,\\
\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,{{\bar v}_{av}} = \frac{{\Delta \bar r}}{{\Delta t}} = \frac{{11\hat i + 11\hat j}}{{5 - 0}} = \frac{{11}}{5}\left( {\hat i + \hat j} \right)
\end{array}\)