Chapter 11 — Introduction to Three Dimensional Geometry

Chapter 11 of the Class 11 Maths NCERT textbook, "Introduction to Three Dimensional Geometry", introduces the 3D coordinate system of three mutually perpendicular axes and planes, representing a point in space by an ordered triplet (x, y, z) and covering distances and octants.

• Extending coordinates into space — The chapter lifts familiar 2D coordinate geometry into three dimensions by adding a third perpendicular axis, so every point in space is now pinned down by three coordinates instead of two.
• Planes, octants and coordinate signs — Three coordinate planes divide space into eight octants, each with its own pattern of signs, and a point's coordinates read as perpendicular distances from those planes — the framework for locating anything in space.
• Measuring distance in 3D — The distance formula generalises to three dimensions, letting you compute separations between points and then verify geometric properties like collinearity and triangle type directly from coordinates.

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