Consider the linear system
a1x + b1y + c1z = d1
a2x + b2y + c2z = d2
a3x + b3y + c3z = d3
of three equations in three unknowns to represent three planes P1, P2, and P3 in xyz-space. Describe the solution set of the system in each of the following cases.
(a) The three planes are parallel and distinct.
(b) The three planes coincide—P1 = P2 = P3.
(c) P1 and P2 coincide and are parallel to P3.
(d) P1 and P2 intersect in a line L that is parallel to P3.
(e) P1 and P2 intersect in a line L that lies in P3.
(f) P1 and P2 intersect in a line L that intersects P3 in a single point.
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