Suppose to have the set of inequalities

$$
\begin{equation}
\begin{aligned}
2x+3y+z\leq5,\\
4x+y+2z\leq11,\\
3x+4y+2z\leq8,\\
x\geq0,\\
y\geq0,\\
z\geq0,\\
\end{aligned}
\end{equation}
$$
and suppose that you want to show the RegionPlot3D associated to it together with the point $(0,0,0)$ (maybe by highlighting the point somehow).

How can you do it?

One last thing: suppose to have multiple points, say (0,0,0), (2.5,0,0), and (2,0,1) and that you want to make a sort of path (0,0,0)-> (2.5,0,0) -> (2,0,1) on the region, how can you do it?