Chapter 11: Three-Dimensional Geometry Class 12 Maths NCERT Solutions | Download Free PDF
Access detailed NCERT Solutions for Class 12 Maths Chapter 11 Three-Dimensional Geometry. Solve questions on lines, planes, angles, and distances with full clarity. Download free PDFs for quick revision and offline practice. Build confidence with step-by-step solved answers. Scroll down for complete chapter content.
Chapter Overview:
Chapter 11, Three Dimensional Geometry, extends your knowledge of coordinate geometry into three-dimensional space. This chapter is essential for visualizing and solving problems involving points, lines, and planes in 3D space—concepts frequently used in physics, engineering, architecture, and computer graphics.
You will learn how to find the direction ratios, direction cosines, and the angle between lines and planes. The concepts are critical for board exams as well as competitive exams like JEE Main, where spatial understanding and geometry-based problem solving are key.
What You’ll Learn in This Chapter:
Introduction to 3D coordinate system
Direction cosines and direction ratios of a line
Equation of a line in space
Angle between two lines
Shortest distance between two skew lines
Equation of a plane
Angle between a line and a plane
Angle between two planes
Why Use These NCERT Solutions:
Our NCERT Solutions for Chapter 11 help students grasp spatial concepts with clarity and confidence. Each question is solved with detailed steps and geometric interpretations so you can:
Build strong spatial visualization skills
Learn precise techniques to solve 3D geometry problems
Tackle both conceptual and calculation-based questions
Score well in CBSE exams and excel in competitive tests
Key Benefits:
Step-by-step solutions to all NCERT exercises
Clear diagrams to support visual understanding
Ideal for last-minute revision and daily practice
Free to access and compatible with all devices
Excellent resource for CBSE and JEE Main preparation