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.Misc.Q.19

Find the vector equation of the line passing through (1, 2, 3) and parallel to the planes r.(i – j + 2k) = 5 and r.(3i + j + k) = 6

Let the required line be parallel to vector b is given by,

b = b₁i + b₂j + b₃k

The position vector of the point (1, 2, 3) is a = i + 2j + 3k

The equation of line passing through (1, 2, 3) and parallel to b is given by,

r = a + λb

=> r = (i + 2j + 3k) + λ(b₁i + b₂j + b₃k) ………..1

The equations of planes are:

r.(i – j + 2k) = 5 ………2

and r.(3i + j + k) = 6 ………3

The line in equation 1 and plane in equation 2 are parallel.

Therefore, the normal to the plane of equation (2) and the given line are perpendicular.

=> (i – j + 2k). λ(b₁i + b₂j + b₃k) = 0

=> λ(b₁ - b₂ + 2b₃) = 0

=> b₁ - b₂ + 2b₃ = 0 ………..4

Similarly, (3i + j + k). λ(b₁i + b₂j + b₃k) = 0

=> λ(3b₁ + b₂ + b₃) = 0

=> 3b₁ + b₂ + b₃ = 0 ………..5

From equations (4) and (5), we get

Therefore, the direction ratios are −3, 5, and 4.

So, b = b₁i + b₂j + b₃k = -3i + 5j + 4k

Put value of b in equation 1, we get

r = (i + 2j + 3k) + λ(-3i + 5j + 4k)

This is the equation of the required line.

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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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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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.