CBSE Ch 11 Important Questions Class 12 Maths 2025 PDF

Three-dimensional geometry (3D Geometry) is a crucial and high-scoring chapter in the Class 12 Mathematics syllabus. It plays a significant role in various real-world applications, including physics, engineering, architecture, and computer graphics.

These important questions help students:

• Understand fundamental concepts
• Develop strong problem-solving skills
• Boost confidence in tackling difficult problems

Many students find Three-Dimensional Geometry challenging during board exams and competitive exams such as JEE, NDA, and state-level entrance tests. To master this topic, practising Class 12 3D Geometry Important Questions and Solutions PDF along with Extra Questions is essential.

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In the table below, we have provided the links to 3D Geometry Class 12 Maths Important Questions PDFs for Chapter 11. You can download them without having to share any login info.

Topics Covered in Class 12 Three-Dimensional Geometry

Understanding 3D Geometry is essential for mastering this chapter in Class 12 Mathematics. As the name suggests, it deals with concepts related to three-dimensional space and includes the following key topics:

Basics of 3D Geometry

• Understanding the 3D coordinate system
• Representing a point in three-dimensional space

Direction Cosines and Direction Ratios

• Definitions and formulas
• Differences between direction cosines and direction ratios

Equations of Lines in 3D Space

• Vector and Cartesian forms of a line’s equation
• Relationship between two lines in 3D
• Finding the shortest distance between two skew (non-parallel) lines

Equations of Planes

• Different forms of plane equations: Intercept, Normal, and General form
• Angle of inclination between two planes
• Inclination of a straight line with a plane
• Determining the position of a point in a plane

Coplanarity of Two Lines

• Condition for two lines to lie in the same plane

Distance Between Two Skew Lines

• Finding the minimum distance between two lines
• Formulating the equation for minimum separation

Intersection of a Line and a Plane

• Checking the possibility of an intersection
• Finding the point of intersection

Why Should You Practise These Important Questions?

Practising Three-Dimensional Geometry Important Questions helps students:

• Strengthen their understanding of core concepts
• Improve problem-solving skills for board and entrance exams
• Gain confidence in solving complex 3D geometry problems
• Learn shortcut techniques to save time during exams

Mastering this chapter is crucial for JEE, NDA, and other competitive exams, as well as for scoring well on board exams. Regular practice ensures a solid grasp of concepts and better exam performance! 

Important Questions and Answers

Important questions related to 3-D Geometry are mentioned below

Q1: Find the equation of the plane passing through (1, 2, 3) and perpendicular to the line with direction ratios (2, -1, 1).

Solution:

The normal to the plane has direction ratios (2, -1, 1).

Using the general equation of a plane:

a(x−x1)+b(y−y1)+c(z−z1)=0

where (a, b, c) = (2, -1, 1) and (x₁, y₁, z₁) = (1, 2, 3).

2(x−1)−1(y−2)+1(z−3)=0

Thus, the required equation of the plane is:

2x−y+z=3

Q2: Find the shortest distance between the skew lines

(x−1)/2=(y+1)/-3=(z-2)/4

or (x−3)/1=(y-2)/-1=(z+4)/2

The direction vectors of the given lines are:

b1​=(2,−3,4),b2​=(1,−1,2)

A point on the first line: (1, -1, 2)

A point on the second line: (3, 2, -4)

The shortest distance d between two skew lines is given by the formula:

d= |(a2​−a1​)⋅(b1​×b2​)∣​/|(b2​−b1​)|

where a₁ = (1, -1, 2) and a₂ = (3, 2, -4).

By applying the formula and solving, we obtain the shortest distance.

Benefits of Practicing 3D Geometry in Class 12

Studying 3D geometry in Class 12 offers multiple advantages, helping students excel in board exams and competitive tests. Below are some key benefits of using 3D Geometry Class 12 notes and important questions:

Improves Preparedness for Board Exams

• Regular practice enhances understanding, making students more confident during their final board examinations.
• Solving different types of important and extra questions ensures familiarity with exam patterns.

Comprehensive Coverage of the Syllabus

• The important questions cover all essential topics, ensuring no concept is left out.
• Students get a clear understanding of formulas, derivations, and applications in 3D Geometry.

Helps in Preparation for Competitive Exams (JEE, NDA, etc.)

• Apart from board exams, 3D Geometry is crucial for JEE, NDA, and other entrance tests.
• Practicing advanced application-based questions gives students a strong foundation.

Enhances Reasoning and Logical Thinking

• Three-dimensional geometry requires spatial visualisation and logical analysis.
• Regular problem-solving sharpens analytical skills and improves mathematical reasoning.

Exposure to Different Levels of Problems

• 3D Geometry consists of basic, intermediate, and advanced-level questions.
• Practicing a variety of problems helps students adapt to different levels of difficulty.

Why Students Should Download These Notes

Here’s why these chapter notes are essential for last-minute revisions:

Efficient Time Management & Planning

• Instead of searching multiple sources, a compiled PDF saves time and allows for a structured revision plan.

Focus on Important Exam Topics

• These notes include important questions based on past exam trends, covering a wide range of problem types.

Improves Problem-Solving Skills

• Regular practice helps students develop efficient and faster problem-solving techniques.

Reduces Exam Stress

• A well-structured set of questions ensures efficient revision, minimising last-minute panic.

Enhances Critical Thinking

• By solving a variety of concept-based and application-based questions, students develop a deeper understanding of 3D Geometry

How to Effectively Use These Notes

Find out how students can use these notes effectively. 

Start with Concept-Based Questions

• First, understand the fundamental theories before moving on to complex numerical problems.

Categorise Questions by Difficulty Level

• Easy: Formula-based, direct application.
• Medium: Multi-step problems integrating different concepts.
• Hard: HOTS (Higher-Order Thinking Skills) & real-life application problems.

Provide Detailed Written Solutions

• Always write step-by-step solutions, as board exams follow a step-marking system.

Identify & Avoid Common Errors

• While solving extra questions, focus on mistakes in calculations and misinterpretation of formulas.

Use Diagrams for Better Understanding

• Since this chapter involves spatial concepts, drawing visual representations can help in grasping concepts better.

Revise Frequently with Short Notes

• Condense formulas & concepts into quick reference notes for efficient last-minute revision.

How to Score High Marks Using These Notes?

Build Strong Conceptual Understanding

Before solving problems, ensure you fully grasp:

• 3D coordinate systems & representation of points.
• Direction cosines & direction ratios.
• Equations of planes & lines in 3D space.

Regularly Practise Important Questions

• Solving frequently asked and extra questions ensures familiarity with different exam question patterns.

Focus on Extra Questions for Competitive Exams

• Extra questions help tackle challenging problems and prepare students for board & entrance exams (JEE, NDA, etc.).

Master Key Formulas & Theorems

Create a formula sheet and revise daily. Important formulas include:
✔ 3D Distance Formula
✔ Section & Midpoint Formula
✔ Angle Between Two Lines or Planes
✔ Different Forms of the Equation of a Plane

The chapter on Three-Dimensional Geometry is crucial for scoring high marks in Class 12 Mathematics. By following a structured study plan and consistently practising important questions, students can strengthen their problem-solving skills and boost their confidence.

Wishing you all the best in your Class 12 exams! Keep practising and stay focused!