Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry – Revision Notes

Three-dimensional coordinate geometry extends the familiar x-y plane with a third axis, splitting space into eight octants instead of four quadrants. Chapter 11 of Class 11 Maths covers how a point is located in this system and how the distance and section formulas adapt to it.

Last Updated: September 23, 2026

3D Coordinate System

• 3 mutually perpendicular axes (x,y,z); origin (0,0,0).
• 8 octants (vs 4 quadrants in 2D).
• Point = ordered triple (x,y,z).

Distance Formula

• d = √[(x2−x1)²+(y2−y1)²+(z2−z1)²].

Section Formula

• Ratio m:n: [(mx2+nx1)/(m+n), (my2+ny1)/(m+n), (mz2+nz1)/(m+n)].

One-Line Summary

3D coordinate geometry extends 2D concepts with a third (z) axis, dividing space into 8 octants, using natural extensions of the distance and section formulas.

Quick visual: a worked diagram from the full Solutions page, for reference.

Frequently Asked Questions

How is a point located in three-dimensional space?
A point in 3D space is located using three coordinates x, y and z, representing its distances from three mutually perpendicular coordinate planes, extending the two-coordinate system used in plane geometry.

What is the distance formula in three dimensions, and how does it relate to the 2D distance formula?
The 3D distance formula is the square root of the sum of squares of differences in the x, y and z coordinates. It is a direct extension of the 2D distance formula with an added z-term.

Written by Satish

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