NCERT solution Class 12 three dimensional geometry

NCERT Solutions

Class 12 Maths

Three Dimensional Geometry

NCERT Questions

Ex.11.1 Q.1
Ex.11.1 Q.2
Ex.11.1 Q.3
Ex.11.1 Q.4
Ex.11.1 Q.5
Ex.11.2 Q.1
Ex.11.2 Q.2
Ex.11.2 Q.3
Ex.11.2 Q.4
Ex.11.2 Q.5
Ex.11.2 Q.6
Ex.11.2 Q.7
Ex.11.2 Q.8
Ex.11.2 Q.9
Ex.11.2 Q.11
Ex.11.2 Q.11
Ex.11.2 Q.12
Ex.11.2 Q.13
Ex.11.2 Q.14
Ex.11.2 Q.15
Ex.11.2 Q.16
Ex.11.2 Q.17
Ex.11.3 Q.1
Ex.11.3 Q.2
Ex.11.3 Q.3
Ex.11.3 Q.4
Ex.11.3 Q.5
Ex.11.3 Q.6
Ex.11.3 Q.7
Ex.11.3 Q.8
Ex.11.3 Q.9
Ex.11.3 Q.10
Ex.11.3 Q.11
Ex.11.3 Q.12
Ex.11.3 Q.13
Ex.11.3 Q.14
Ex.Misc. Q.1
Ex.Misc.Q.2
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10
Ex.Misc.Q.11
Ex.Misc.Q.12
Ex.Misc.Q13
Ex.Misc.Q.14
Ex.Misc.Q.15
Ex.Misc.Q.16
Ex.Misc.Q.17
Ex.Misc.Q.18
Ex.Misc.Q.19
Ex.Misc.Q.20
Ex.Misc.Q.21
Ex.Misc.Q.22
Ex.Misc.Q.23

Ex.11.2 Q.11

Find the angle between the following pairs of lines:

(i)

(ii)

(i) Let b₁ and b₂ be the vectors parallel to the pair of lines,

So, b₁ = 2i + 5j - 3k and b₂ = -i + 8j + 4k

Now, |b₁| = √{2² + 5² + (-3)²} = √(4 + 25 + 9) = √(38)

And |b₂| = √{(-1)² + 8² + 4²} = √(1 + 64 + 16) = √(81) = 9

Now, b₁ . b₂ = (2i + 5j - 3k).(-i + 8j + 4k)

= -2 * 1 + 5 * 8 - 3 * 4

= -2 + 40 - 12

= 26

The angle, Q, between the given pair of lines is given by the relation,

cos Q =

=> cos Q =

=> Q = cos^-1

(ii) Let b₁ and b₂ be the vectors parallel to the pair of lines,

So, b₁ = 2i + 2j + k and b₂ = 4i + j + 8k

Now, |b₁| = √{2² + 2² + (-1)²} = √(4 + 4 + 1) = √9 = 3

And |b₂| = √{4² + 1² + 8²} = √(16 + 1 + 64) = √(81) = 9

Now, b₁ . b₂ = (2i + 2j + k).(4i + j + 8k)

= 2 * 4 + 2 * 1 + 1 * 8

= 8 + 2 + 8

= 16

The angle, Q, between the given pair of lines is given by the relation,

cos Q =

=> cos Q =

=> Q = cos^-1

Three Dimensional Geometry Class 12 Maths NCERT Chapter 11 NCERT Solutions

Solving NCERT textbook questions of Three Dimensional Geometry Class 12 Maths NCERT Chapter 11 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 12 Maths Three Dimensional Geometry, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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How to make the most of NCERT Solutions module of Three Dimensional Geometry Class 12 Maths NCERT Chapter 11 on LearnoHub.com?

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 12 Maths Three Dimensional Geometry Online Test on LearnoHub.com.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Three Dimensional Geometry Class 12 Maths Notes.
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NCERT solutions of Three Dimensional Geometry Class 12 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 12 Maths Three Dimensional Geometry NCERT solutions.