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NCERT Solutions for Class 12 Maths Chapter 11 – Three Dimensional Geometry Exercise 11.2

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Chapter 11 – Three Dimensional Geometry Exercise 11.2

1.

NCERT Class 12 Exercise 11.2 question on angle between two lines-Q1

Sequential resolution for the angle between lines – NCERT Exercise 11.2 Question 1

Final values of direction cosines and angle for Q1 from Class 12 Geometry

2.

Problem involving shortest distance between skew lines – Class 12 Geometry-Q2

Answer image showing shortest distance formula applied – Exercise 11.2 Q2

3.

3D Geometry problem from Exercise 11.2 related to line intersection-Q3

Solution using line intersection method in 3D Geometry – Exercise 11.2 Q3

Final intersection point and vector values for Q3 NCERT Class 12

4.

Line and point position-based problem – NCERT Exercise 11.2 Q4

Class 12 Geometry Q4 solution involving point on a line in space

5.

Distance of a point from a line in 3D space – Exercise 11.2 Q5

Steps to find perpendicular distance from point to line – Q5 Answer

6.

Class 12 3D Geometry Exercise 11.2 Question 6- NCERT-Q6

Class 12 Q6 solution for checking perpendicular lines using dot product

7.

Vector projection problem from Exercise 11.2 – NCERT Class 12-Q7

Answer image using vector projection to find distance – Q7 Class 12

8.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 8- testing vector cross product in geometry-NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 8 Answer showing resultant perpendicular vector-2 - NCERT Answer

9.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 9- angle between lines using dot product-NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 9 Solution using dot product to find angle -1 - NCERT Answer-1

10.

Class 12 3D Geometry Exercise 11.2 Question 10- Shortest distance between two given lines-NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 10 Stepwise working for shortest distance between skew lines- NCERT Answer

11.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 11 - problem involving skew lines and their orientation-NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 11 Skew line concept application- NCERT Answer

12.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 12- finding coordinates of foot of perpendicular- NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 12 Answer showing coordinates of perpendicular foot from point to line- NCERT Answer

13.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 13 - Angle and distance from origin to line -NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 13 Detailed answer image finding angle and distance from origin- NCERT Answer

Class 12 Three Dimensional Geometry Exercise 11.2 Question 13 Final result and simplified vector expression - NCERT Answer

14.

Class 12 Three Dimensional Geometry Exercise 11.2 Question 14-Position vector-based question- NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 14 answer using vector components and parametric form
- NCERT Answer

Class 12 Three Dimensional Geometry Exercise 11.2 Question 14 Final solution with line equation- NCERT Answer

15.

Class 12 3D Geometry Exercise 11.2 Question 15-direction ratios and shortest distance - NCERT

Class 12 Three Dimensional Geometry Exercise 11.2 Question 15 Shortest distance formula with vector subtraction- NCERT Answer

Class 12 Three Dimensional Geometry Exercise 11.2 Question 15 simplified result - NCERT Answer

Class 12 Three Dimensional Geometry Exercise 11.2 Question 15 Solution - NCERT Answer

Download Exercise 11.2 NCERT Solutions PDF

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Download Chapter 11 – Three Dimensional Geometry NCERT Solutions PDF

Class 12 Maths Chapter 11 – Three Dimensional Geometry: All Exercises

Exercise	Link
Exercise 11.1	View Solutions

Class 12 Three Dimensional Geometry- Exercise 11.2 Overview

Exercise 11.2 of 3D Geometry Class 12 NCERT Solutions introduces the idea of coplanarity and the angle between two lines, therefore deepening spatial comprehension. Following line equations in Exercise 11.1, this section clarifies how two lines interact in space—that is, whether they intersect, are parallel, or are skew (non-intersecting and non-parallel). Especially when working on geometry-based reasoning difficulties, this is a vital ability.

This assignment highlights using vector ideas to geometry in three dimensions per the 2025 revised NCERT syllabus. Working with dot products, you will find perpendicular lines, calculate angles between lines, and find whether two lines lie in the same plane. Even if you’re not very experienced with 3D visuals yet, our Three Dimensional Geometry Class 12 NCERT Solutions Exercise 11.2 provides step-by-step support to help you fully understand these applications.

Although many students mix the angle between vectors with that between lines, this exercise uses actual examples to make clear that difference. You’ll also learn to verify coplanarity, an important topic when solving advanced geometry or engineering problems. Our solutions in Chapter 11 guarantee that you understand the reasoning behind every action rather than only fix the issues.

Completely lays the groundwork for future subjects like distance between lines and planes in 3D space by doing Three Dimensional geometry class 12 NCERT solutions exercise 11.2. This practice helps one to grasp how objects exist and relate in the real world, not only regarding tests.

FAQs – Three Dimensional Geometry Class 12 Exercise 11.2 NCERT

In 3D geometry, what does Exercise 11.2 target?

It addresses how to find whether two lines are coplanar in 3D space as well as angles between lines.

How in 3D can I find the angle between two lines?

You determine the angle by applying the cosine formula using the dot product of the lines’ direction vectors.

What is coplanarity, and why is it significant?

Two lines or vectors are said to be coplanar—that is, on the same plane. Spatial thinking is fundamental in geometry, engineering, and physics.

Describe the variations among parallel, intersecting, and skew lines?

Parallel: same path; never cross
Intersecting: get together at a point.
Skew: not parallel and not intersecting

Can these problems appear in JEE or CUET exams?

Most definitely! Engineering entrance tests abound in angle and coplanarity questions.

Where can I obtain revised and resolved Exercise 11.2’s problems?

Cogniks.com offers all free step-by–step 3D geometry class 12 NCERT solutions exercise 11.2.