NCERT Class 11 Mathematics Mathematics: Chapter 11 — MATHEMATICS
This chapter introduces the fundamental concepts of three-dimensional geometry. It explains the need for three coordinates to locate a point in space, unlike the two coordinates required for a plane. The chapter defines coordinate axes (x, y, z) and coordinate planes (XY, YZ, ZX) formed by three mutually perpendicular planes intersecting at the origin. It details how these planes divide space into eight octants. The process of assigning coordinates (x, y, z) to a point P in space is explained by dropping a perpendicular from P to the XY-plane and then drawing a perpendicular from that point to the x-axis. The chapter lays the groundwork for understanding geometric concepts in a 3D environment, crucial for advanced mathematics and science applications.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 11 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 11 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 732 |
Learning outcomes
- Understand the necessity of three coordinates for locating points in space.
- Define and identify coordinate axes (x, y, z) and coordinate planes (XY, YZ, ZX).
- Recognize the origin as the intersection of the coordinate planes.
- Understand that the coordinate planes divide space into eight octants.
- Learn how to determine the coordinates (x, y, z) of a point in space.
Vocabulary
| Word | Meaning |
|---|---|
| Coordinate axes | Mutually perpendicular lines (x, y, z) that form the basis of a 3D coordinate system. |
| Coordinate planes | Planes formed by pairs of coordinate axes (XY, YZ, ZX). |
| Origin | The point of intersection of the three coordinate axes and planes (0, 0, 0). |
| Octants | The eight regions into which space is divided by the three coordinate planes. |
| Coordinates | Three numbers (x, y, z) that uniquely define the position of a point in space. |
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Practice questions
- Why are three coordinates needed to locate a point in space? Answer: Three coordinates are needed because space has three dimensions (length, width, height), unlike a plane which has only two.
- What are the three coordinate planes? Answer: The three coordinate planes are the XY-plane, YZ-plane, and ZX-plane.
- What is the origin in a 3D coordinate system? Answer: The origin is the point where the three coordinate axes intersect, with coordinates (0, 0, 0).
- How many octants are there in three-dimensional space? Answer: There are eight octants in three-dimensional space.
Practice MCQs
Q1. To locate a point in a plane, how many coordinates are typically needed?
Explanation: In a plane, two mutually perpendicular axes are used, requiring two coordinates to define a point's position.
Q2. Which of the following is NOT a coordinate plane in a 3D system?
Explanation: The standard coordinate planes are formed by pairs of x, y, and z axes, not UV axes.
Q3. The point where the three coordinate axes intersect is called the:
Explanation: The origin is the central point where all three coordinate axes meet in a 3D system.
Q4. How many regions does space get divided into by the three coordinate planes?
Explanation: The three mutually perpendicular coordinate planes divide the entire three-dimensional space into eight distinct regions called octants.
Q5. If a point P has coordinates (x, y, z), what does 'z' represent?
Explanation: The z-coordinate represents the perpendicular distance of the point from the XY-plane.
Frequently asked questions
What is the main difference between locating a point in a plane and in space?
Locating a point in a plane requires two coordinates (x, y), while locating a point in space requires three coordinates (x, y, z) due to the added dimension.
What are the coordinate axes in three-dimensional geometry?
The coordinate axes are three mutually perpendicular lines, denoted as the x-axis, y-axis, and z-axis, intersecting at the origin.
What are coordinate planes?
Coordinate planes are the planes formed by pairs of coordinate axes: the XY-plane, YZ-plane, and ZX-plane.
What is an octant?
An octant is one of the eight regions into which the three coordinate planes divide the three-dimensional space.
How is the z-coordinate of a point determined?
The z-coordinate of a point is its perpendicular distance from the XY-plane.
What does the triplet (x, y, z) represent for a point in space?
The triplet (x, y, z) represents the unique coordinates of a point in space, defining its position relative to the origin and coordinate planes.
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NCERT Class 11 Mathematics — Mathematics — Chapter 11 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.