📐 Cases of Intersection in 3D Space

Case 0: ❌ No Common Intersection

• Two planes intersect in a line, but the third is parallel and does not intersect.
• Or all three planes are parallel but not coincident.
• Result: No solution to the system of equations.

Case 1: 🎯 Unique Point of Intersection

• Two planes must be nonparallel and intersect in a line.
• The third plane must be nonparallel to that line and intersect it at a single point.
• Result: Exactly one solution — the point where all three planes meet.

Case 2: 📏 Intersection Along a Line

• Each pair of planes intersects in a line.
• All three planes share exactly one common line.
• Result: Infinitely many solutions along that line.

Case 3: 🪞 Coincident Planes

• All three planes are the same (fully overlapping).
• Every point on the plane satisfies all three equations.
• Result: Infinitely many solutions filling the entire plane.