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.11.3 Q.3

Find the Cartesian equation of the following planes:

(a) r.(i + j + k) = 2

(b) r.(2i + 3j – 4k) = 1

(a) It is given that equation of the plane is

r.(i + j + k) = 2 ………..1

For any arbitrary point P (x, y, z) on the plane, position vector r is given by,

r = xi + yj + zk

Substituting the value of r in equation 1, we obtain

(xi + yj + zk)(i + j − k) = 2

=> x + y − z = 2

This is the Cartesian equation of the plane.

(b) Given, r. (2i + 3j – 4k) = 1 .......1

For any arbitrary point P (x, y, z) on the plane, position vector r is given by,

r = xi + yj + zk

Substituting the value of r in equation 1, we obtain

(xi + yj + zk)(2i + 3j – 4k) = 1

=> 2x + 3y − 4z = 2

This is the Cartesian equation of the plane.

For any arbitrary point P (x, y, z) on the plane, position vector r is given by,

r = xi + yj + zk

Substituting the value of r in equation 1, we obtain

(xi + yj + zk)[(s − 2t)i + (3 − t)j + (2s + t)k] = 15

=> (s − 2t)x + (3 − t)y + (2s + t)z = 15

This is the Cartesian equation of the plane.

Three Dimensional Geometry Class 12 Maths NCERT Chapter 11 NCERT Solutions

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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.