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Consider the following system of linear equations, where \(a \in \mathbb{R}\):$$\left\{\begin{array}{rcrcrcr} x &+& 2y &-& z &=& 1 \\ 2x &+& 5y &+& z &=& 5 \\ x &+& 3y &+& 2z &=& a\end{array}\right.$$
  1. Find the value of \(a\) for which the system has infinitely many solutions.
  2. For this value of \(a\), find the general solution to the system of equations.
  3. Describe the geometric interpretation of the system for this value of \(a\).

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