NCERT Solutions for Class 12 Maths Chapter 11 Miscellaneous Exercise of 3D Three Dimensional Geometry in Hindi and English Medium for session 2023-24. The question answers and solutions of 12th Maths Misc. ex. 11 are updated according to new NCERT book issued for CBSE 2023-24.

## 12th Maths Chapter 11 Miscellaneous Exercise in Hindi and English

### NCERT Solutions for Class 12 Maths Miscellaneous Exercise 11

Class 12 Maths solutions are updated for session 2023-24 in both language – Hindi and English. These are free to use for all users without any login or password. Videos in Hindi and English medium are also given with PDF solutions.

Class: 12 | Mathematics |

Chapter: 11 | Miscellaneous Exercise 11 |

Topic: | Three Dimensional Geometry |

Contents: | Exercise and Extra Questions |

Content Type: | Text, PDF and Videos |

Session: | CBSE 2023-24 |

Medium: | Hindi and English Medium |

#### Class 12 Maths Chapter 11 Miscellaneous Exercise Solutions

Download CBSE NCERT Solutions for Class 12 Maths Chapter 11 Miscellaneous Exercise 11 in PDF file format free or view online in videos format also. Solutions are available in Hindi and English Medium following the latest NCERT Books for class 12 session 2023-24.

#### Class 12 Maths Miscellaneous Exercise 11 Solution in Videos

#### What is a Plane?

A plane is determined uniquely if any one of the following is known:

- The normal to the plane and its distance from the origin is given, i.e., equation of a plane in normal form.
- It passes through a point and is perpendicular to a given direction.
- It passes through three given non collinear points.

Here, we shall discuss vector and Cartesian equations of the planes.

##### Points to be remembered

- 1. If d is the distance from the origin and l, m, n are the normal cosines of the plane direction through the origin, the foot of the perpendicular is (ld, md, nd).
- 2. Do you know why was it necessary to say that the three points had to be non collinear? If the three points were on the same line, then there will be many planes that will contain them.
- 3. The angle between two planes is defined as the angle between their normal.
- 4. The planes are perpendicular to each other if n1.n2 = 0 and parallel if n1 is parallel to n2.
- 5. The angle between a line and a plane is the complement of the angle between the line and normal to the plane.

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### Which question is important in class 12 Maths chapter 11 Miscellaneous Exercise?

There are almost all the questions are important in miscellaneous exercises 11 of class 12 Maths. So, do each and every question carefully to score better in board exams.

### What are the frequently asked questions from class 12 Maths Chapter 11 Miscellaneous exercise?

Question number 1, 4 and 5 are frequently asked in board exams. There may be the change of digits in questions.