\(\fbox{6}\) Planes that meet on parallel lines (GDC allowed)
Let \[\pi_1: 3x - 2y + z = 10\]
\[\pi_2: 2x + y - 3z = 2\]
The planes \(\pi_1\), \(\pi_2\) and \(\pi_3\) meet along three parallel lines. Find a possible plane \(\pi_3\) in the form \(ax+by+cz=k\)
\[\pi_2: 2x + y - 3z = 2\]
The planes \(\pi_1\), \(\pi_2\) and \(\pi_3\) meet along three parallel lines. Find a possible plane \(\pi_3\) in the form \(ax+by+cz=k\)