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.Q13

Find the equation of the plane passing through the point (−1, 3, 2) and

perpendicular to each of the planes x + 2y + 3z = 5 and 3x + 3y + z = 0.

The equation of the plane passing through the point (−1, 3, 2) is

a(x + 1) + b(y − 3) + c (z − 2) = 0 ......... 1

where, a, b, c are the direction ratios of normal to the plane.

It is known that two planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0 are perpendicular, if a₁a₂ + b₁b₂ + c₁c₂ = 0

Plane 1 is perpendicular to the plane x + 2y + 3z = 5

So, a * 1 + b * 2 + c * 3 = 0

=> a + 2b + 3c = 0 ………..2

Also, plane 1 is perpendicular to the plane 3x + 3y + z = 0

So, a * 3 + b * 3 + c * 1 = 0

=> 3a + 3b + c = 0 ………..3

From equations 2 and 3, we get

=> a-7=b8=c-3= k (say)

=> a = -7k, b = 8k, c = -3k

Substituting the values of a, b, and c in equation 1, we get

-7k(x + 1) + 8k(y - 3) – 3k(z - 2) = 0

=> -7(x + 1) + 8(y - 3) – 3(z - 2) = 0

=> -7x – 7 + 8y – 24 – 3z + 6 = 0

=> 7x – 8y + 3z + 25 = 0

This is the required equation of the plane.

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 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.
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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.