Download Free PDF of Introduction to Three Dimensional Geometry for Class 11 Maths
FAQs on CBSE Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry – NCERT Solutions 2025-26
1. What are the most important formulas in Class 11 Chapter 11 Introduction to Three Dimensional Geometry?
The most important formulas in Class 11 Chapter 11 Introduction to Three Dimensional Geometry focus on coordinates, distance, and sectioning in space:
Key formulas include:
- Distance Formula (3D):
Distance between points A(x₁, y₁, z₁) and B(x₂, y₂, z₂): √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²] - Section Formula (3D):
Point dividing AB in ratio m:n:
P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n)) - Midpoint Formula:
M = ((x₁+x₂)/2, (y₁+y₂)/2, (z₁+z₂)/2)
2. How to understand and visualize 3D geometry concepts for board exams?
To understand and visualize 3D geometry for board exams, practice interpreting points and planes in space using diagrams and real-world analogies.
Follow these tips to grasp 3D concepts:
- Draw coordinate axes (X, Y, Z) to locate points and planes.
- Use arrows and color-coding to differentiate axes and quadrants (octants).
- Relate problems to familiar objects (rooms, boxes) for better spatial orientation.
- Practice solved examples and visual revision mind maps.
- Apply the distance and section formulas stepwise in exercises.
3. Where can I download NCERT solutions PDF for Class 11 Maths Chapter 11?
You can download NCERT solutions PDF for Class 11 Maths Chapter 11 from trusted academic platforms like Vedantu, ensuring syllabus compliance and full coverage.
Key benefits of using verified PDFs:
- All stepwise solutions to textbook questions (including miscellaneous exercises).
- Easy offline access for quick revision before board exams and competitive tests.
- Syllabus-aligned, exam-focused answers for high scores.
4. How do I solve Miscellaneous Exercise in Chapter 11 effectively?
To solve the Miscellaneous Exercise in Class 11 Maths Chapter 11 effectively, focus on concept clarity and systematic application of key formulas.
Steps for success:
- Review all formulas before starting.
- Read each question carefully and identify the required concepts (e.g., distance, section, coordinates).
- Draw a rough diagram to visualize spatial relationships.
- Write stepwise solutions, explicitly mentioning substitutions and calculations.
- Compare your approach with NCERT-supplied stepwise solutions for accuracy.
5. Are the stepwise solutions provided suitable for JEE preparation as well?
Yes, the stepwise solutions for Class 11 Maths Chapter 11 (3D Geometry) are highly suitable for JEE preparation.
Advantages for JEE aspirants:
- Cover all fundamental concepts and formulas relevant to competitive exams.
- Provide logically ordered, exam-style steps that mirror JEE question solving.
- Help develop strong spatial reasoning and problem-solving skills needed for Higher Mathematics.
6. What tips should I follow for last-minute revision of 3D geometry?
For last-minute revision of 3D geometry, focus on formulas and key properties.
Follow this quick checklist:
- Revise the distance, section, and midpoint formulas.
- Review all solved NCERT examples with attention to steps.
- Practice important questions from the miscellaneous exercise.
- Refer to a formula sheet or mind map for fast recall.
- Attempt a short timed quiz to boost speed and accuracy.
7. What is the section formula in 3D geometry?
The section formula in 3D geometry finds the coordinates of a point dividing a line segment in a given ratio in space.
For points A(x₁, y₁, z₁) and B(x₂, y₂, z₂) divided by P in the ratio m:n:
P = ((mx₂ + nx₁)/(m+n), (my₂ + ny₁)/(m+n), (mz₂ + nz₁)/(m+n))
Use this to solve NCERT and JEE line division questions in 3D geometry.
8. What is a three-dimensional coordinate system?
A three-dimensional coordinate system is a way to locate points in space using three axes: X, Y, and Z.
Main features:
- Axes: X (horizontal), Y (vertical), Z (perpendicular to X and Y)
- Every point represented as (x, y, z)
- Helps visualize spatial problems involving distance, planes, and position
- Essential for topics like 3D geometry, vectors, and physics
9. What is the distance formula in 3D geometry?
The distance formula in 3D geometry calculates the straight-line distance between two points in space.
If A(x₁, y₁, z₁) and B(x₂, y₂, z₂), then:
Distance = √[(x₂-x₁)² + (y₂-y₁)² + (z₂-z₁)²]
This formula appears in nearly every board and JEE exam for Class 11 Maths Chapter 11.
10. How can I get full marks in maths 11th?
To get full marks in Maths Class 11, focus on clarity, revision, and practice.
Follow these steps:
- Study all NCERT solutions for each chapter, especially exercises and miscellaneous sections.
- Memorize and practice all important formulas and theorems.
- Solve previous year question papers and practice MCQs.
- Revise with summary notes, mind maps, and diagrams.
- Clarify all doubts promptly, and practice time management in exams.

















