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.2

Show that the line through the points (1, −1, 2) (3, 4, −2) is perpendicular to the line through the points (0, 3, 2) and (3, 5, 6).

Let AB be the line joining the points, (1, −1, 2) and (3, 4, − 2), and CD be the line joining the points, (0, 3, 2) and (3, 5, 6).

The direction ratios, a₁, b₁, c₁ of AB are (3 − 1), (4 − (−1)), and (−2 − 2) i.e., 2, 5 and −4.

The direction ratios, a₂, b₂, c₂ of CD are (3 − 0), (5 − 3), and (6 −2) i.e., 3, 2, and 4.

AB and CD will be perpendicular to each other, if a₁a₂ + b₁b₂+ c₁c₂ = 0

Now, a₁a₂ + b₁b₂+ c₁c₂= 2 * 3 + 5 * 2 + (− 4) * 4

= 6 + 10 − 16

= 0

Therefore, AB and CD are perpendicular to each other.

Three Dimensional Geometry Class 12 Maths NCERT Chapter 11 NCERT Solutions

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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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By following these steps and actively engaging with the NCERT solutions module of Class 12 Maths Three Dimensional Geometry NCERT Chapter 11, you can improve your learning outcomes, develop a better grasp of the subject, and perform well in exams and other academic assessments. Remember that consistent practice, understanding, and application of knowledge are key to academic success.

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.