Chapter 11 — Introduction to Three Dimensional Geometry

Chapter 11 introduces the three-dimensional coordinate system using three mutually perpendicular axes and planes. A point in space is represented by an ordered triplet (x, y, z), and key topics include locating points using coordinates, finding distances between points, and identifying the eight octants formed by coordinate planes.

Introduction to Three Dimensional Geometry extends two-dimensional coordinate geometry to three-dimensional space. The chapter establishes a rectangular coordinate system with three mutually perpendicular axes (x, y, z) and three coordinate planes (XY, YZ, ZX) that divide space into eight octants. Each point in space has three coordinates representing perpendicular distances from the three coordinate planes. The distance formula between two points P(x₁, y₁, z₁) and Q(x₂, y₂, z₂) is derived as: PQ = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]. Applications include determining collinearity, classifying triangles, and finding geometric relationships between points.

1. 01Three-dimensional space uses three mutually perpendicular coordinate axes (x, y, z) that meet at the origin O
2. 02The three coordinate planes (XY, YZ, ZX) divide space into eight octants, each with distinct sign patterns for coordinates
3. 03A point P(x, y, z) has coordinates representing perpendicular distances from the YZ, ZX, and XY planes respectively
4. 04Distance between two points is calculated using PQ = √[(x₂−x₁)² + (y₂−y₁)² + (z₂−z₁)²]; distance from origin to Q(x, y, z) is √(x² + y² + z²)
5. 05Points lying on axes have two zero coordinates; points in coordinate planes have one zero coordinate
6. 06The distance formula enables verification of geometric properties like collinearity, triangle types, and quadrilateral shapes