NCERT Solutions for Class 11 Mathematics Chapter Introduction to Three Dimensional Geometry

This worksheet is designed to help students understand the basics of three dimensional geometry in Class 11 Mathematics. The chapter Introduction to Three Dimensional Geometry explains how to locate points in space using three coordinates and understand their positions with respect to coordinate planes and axes. This concept is important as it forms the foundation for advanced geometry and spatial reasoning. This worksheet provides complete and accurate NCERT Solutions, strictly following the NCERT structure and exercises.It focuses on understanding spatial geometry using coordinate axes and planes. Students learn how to identify octants, locate points in space, and calculate distances between points. The chapter is mainly numerical and concept-driven, with visual understanding through diagrams and coordinate systems.

What this NCERT chapter covers?

• Understanding coordinate axes and coordinate planes in 3D 
• Identifying coordinates of a point in space 
• Learning about octants and sign conventions 
• Finding distance between two points using formula 
• Verifying geometric properties like collinearity and triangle types 
• Solving algebraic equations based on distance conditions 

How to use these NCERT solutions?

Students should first attempt all questions in the worksheet on their own to build understanding. After attempting, they can use these NCERT Solutions to verify answers and correct mistakes. Parents and teachers can use these solutions to guide students and ensure correct methods are followed. The solutions are arranged exactly in NCERT order, which helps in structured learning and easy revision.

Student tips & learning tricks

• Always check the sign of coordinates before identifying octants 
• Use the distance formula carefully and avoid calculation errors 
• Practice identifying coordinate planes clearly 
• Revise formulas regularly to avoid confusion 
• Double-check algebraic simplifications in equations

 Why NCERT solutions are important?

NCERT Solutions are essential because they follow the exact CBSE curriculum and exam pattern. They help students build strong conceptual understanding and improve problem-solving skills. These solutions ensure accuracy, boost confidence, and prepare students effectively for school exams and competitive assessments.

Complete answer key – NCERT solutions

Exercise 11.1

1 
y-coordinate = 0 
z-coordinate = 0 

2 
y-coordinate = 0 

3 
1. I octant 
2. IV octant 
3. V octant 
4. V octant 
5. VI octant 
6. II octant 
7. III octant 
8. VII octant 

4 
1. XY-plane 
2. (x, y, 0) 
3. 8 

Exercise 11.2

1 
1. √20 
2. √43 
3. √104 
4. √20 

2 
Points are collinear 

3 
1. Isosceles triangle 
2. Right angled triangle 
3. Parallelogram 

4 
x – 2z – 1 = 0 

5 
x² + y² + z² = 9 

Miscellaneous Exercise

1 
(1, –2, 8) 

2 
√52, √52, √52 

3 
a = –2 
b = –1 
c = 3 

4 
2x² + 2y² + 2z² – 4x – 14y + 4z = k² – 109 

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