NCERT Solutions for Class 12 Maths Chapter 11 Miscellaneous Exercise 11 of 3D geometry or Three Dimensional Geometry in Hindi and English Medium free to use online or download in PDF file format. Class 12 Maths solutions are updated for session 2022-2023 in Hindi and English Medium. These are free to use for all users without any login or password. Videos in Hindi and English medium is also given with PDF solutions.

## NCERT Solutions for Class 12 Maths Miscellaneous Exercise 11

### NCERT Solutions for Class 12 Maths Miscellaneous Exercise 11 in Hindi and English Medium

Class: 12 | Mathematics |

Chapter: 11 | Miscellaneous Exercise 11 |

Contents: | NCERT Solutions in 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 2022-2023.

### 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 13, 16 and 17 are frequently asked in board exams. There may be the change of digits in questions.