本题目来源于试卷: Systems of Equations，类别为 IB数学
[问答题]
Consider three planes represeslf gt.n ,3pbv xj.rs8:/j g3qnt1(a n,cjb,peu3ry, - -vd fogted by the following system of equations:
$\begin{array}{c}
\Pi_{1}:-2 x+a y+4 z=2 \\
\Pi_{2}: x+b y-2 z=-1 \\
\Pi_{3}: 2 x-y+c z=3
\end{array}
$
Where $ a, b, c \in \mathbb{R}$.
1. State the values of a, b and c for which
1. The system has infinite solutions.
2. The system is inconsistent.
2. In the case where the system has infinite solutions, describe the geometric relationship between the three planes.
3. In the case where the system is inconsistent, identify one of the geometric relationships that could exist between the three planes.
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