Chapter 11 - Three-Dimensional Space; Vectors - 11.6 Planes in 3-Space - Exercises Set 11.6 - Page 821: 55

Two planes: $0$, $\infty$ intersection points Three planes: $0$, $\infty$ intersection points

Two planes having a set of common points simply means they are mutually positioned. The manner in which they mutually interact describes the set of points that they have in common: Coincident: $\infty$ solutions Intersecting: the common points between the two planes will be described by a line; still has $\infty$ solutions Parallel: no solution For three planes: All planes are parallel to each other: no solution. Two planes are parallel to each other: no solution. Three intersecting planes have no common intersection: no solution Three coincident planes: $\infty$ solutions Three planes intersecting in a line: described by a line, $\infty$ solutions Three planes intersecting at a point: described by a point, one solution Two coincident planes intersecting with a plane: a line, so $\infty$ solutions Two coincident planes parallel to a plane: no solution