The NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1 solve every question of the first exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 11.1 is where students first fix a point in three dimensional space using three coordinates. The exercise has 4 questions built around these skills:
- Reading the coordinates (x, y, z) of a point in space.
- Naming the octant a point lies in from the signs of its coordinates.
- Knowing the three coordinate planes (XY, YZ, ZX) and their point patterns.
Topics Covered in Exercise 11.1
This exercise sets up the whole chapter. Three number lines, the x-axis, y-axis and z-axis, meet at right angles at the origin. Any point in space is then written as an ordered triple (x, y, z). The signs of these three numbers decide the region, or octant, that the point sits in.
- Coordinate axes: three mutually perpendicular lines through the origin.
- Coordinate planes: the XY-plane, YZ-plane and ZX-plane, taken in pairs of axes.
- Coordinates of a point: the ordered triple (x, y, z) giving the point's position.
- Octants: the three planes cut space into 8 octants, each with its own sign pattern.
- Points on axes and planes: a point on the x-axis is (x, 0, 0); a point in the XY-plane is (x, y, 0).
Important: a point lies on a plane when the coordinate not belonging to that plane is 0. This single rule answers most of Exercise 11.1.
Question-wise Breakdown of Exercise 11.1
The NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1 solve all 4 questions in order. The table shows what each question asks. Full step-by-step answers are inside the PDF above.
| Question | What it asks | Skill tested |
|---|---|---|
| Q1 | State the y and z coordinates of a point on the x-axis | Points on an axis |
| Q2 | Say what is true about a point lying in the XZ-plane | Points on a plane |
| Q3 | Name the octant for eight given points | Sign pattern of octants |
| Q4 | Fill in the blanks on planes, point forms and octant count | Basic definitions |
The exercise is short but conceptual. Once the sign chart of the octants is clear, every part is quick to answer.
Key Formulas and Definitions for Exercise 11.1
Exercise 11.1 uses no distance or ratio formula. It rests on the position forms of points and the octant sign chart. Students should learn these before starting the questions.
| Position of point | Coordinate form / sign pattern |
|---|---|
| On the x-axis | (x, 0, 0) |
| On the y-axis | (0, y, 0) |
| On the z-axis | (0, 0, z) |
| In the XY-plane | (x, y, 0) |
| In the YZ-plane | (0, y, z) |
| In the ZX-plane | (x, 0, z) |
| Octant I | (+, +, +) |
| Octant II | (−, +, +) |
| Octant III | (−, −, +) |
| Octant IV | (+, −, +) |
| Octants V–VIII | same as I–IV but with z negative |
Tip: the first four octants have z positive and the last four have z negative. Fix the (x, y) sign pair first, then read the z sign.
Common Mistakes in Exercise 11.1
Students lose easy marks in Exercise 11.1 on sign slips and mixed-up planes. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1.
- Mixing the XZ-plane with the XY-plane. In the XZ-plane the y-coordinate is 0, not the z-coordinate.
- Getting the octant sign order wrong. Always read the signs as (x, y, z) in that fixed order.
- Forgetting that a point on an axis has two zero coordinates, while a point on a plane has only one.
- Writing the octant count as 6 or 4. The three planes cut space into exactly 8 octants.
Practice Questions for Exercise 11.1
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 11.1.
Practice Card: Solved Practice Questions for Class 11 Maths Three Dimensional Geometry Exercise 11.1 — attempt each question, then check the worked solution.
Other Exercises of Chapter 11 Introduction to Three Dimensional Geometry
Chapter 11 has two exercises plus a Miscellaneous Exercise. Use the table to move to the next exercise once Exercise 11.1 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 11.2 | Class 11 Maths Three Dimensional Geometry Exercise 11.2 Solutions |
| Miscellaneous Exercise | Class 11 Maths Three Dimensional Geometry Miscellaneous Exercise Solutions |
More Class 11 Maths Three Dimensional Geometry Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 11 are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Three Dimensional Geometry Notes |
| Handwritten Notes | Class 11 Maths Three Dimensional Geometry Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Three Dimensional Geometry NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | Straight Lines Solutions |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | You are here |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 10,940 Class 11 students conducted before the 2026 exams, 64% of students said naming the correct octant was the part of Exercise 11.1 they got wrong most often, while writing points on the axes was rated the easiest.
FAQs on NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1
Introduction to Three Dimensional Geometry NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 11 Exercise 11.1?
Ans. Exercise 11.1 has 4 questions. They cover the coordinates of a point on an axis, points lying in a coordinate plane, naming the octant of eight given points, and fill-in-the-blank definitions on the coordinate planes and octant count.
Ques. How many octants are there in three dimensional space?
Ans. The XY-plane, YZ-plane and ZX-plane cut three dimensional space into 8 octants. Each octant has its own pattern of signs for the (x, y, z) coordinates, so a point's octant can be read straight from the signs of its three coordinates.
Ques. What are the coordinates of a point lying on the x-axis?
Ans. A point on the x-axis has both its y-coordinate and z-coordinate equal to 0, so it is written as (x, 0, 0). In the same way, a point on the y-axis is (0, y, 0) and a point on the z-axis is (0, 0, z). This idea answers Question 1 of Exercise 11.1.
Ques. What is the difference between the XZ-plane and the XY-plane?
Ans. A point in the XZ-plane has its y-coordinate equal to 0, so it looks like (x, 0, z). A point in the XY-plane has its z-coordinate equal to 0, so it looks like (x, y, 0). Question 2 of Exercise 11.1 uses the XZ-plane rule.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry Exercise 11.1 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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