# NCERT Solutions for Class 11 Maths Chapter 12

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry in English and Hindi Medium for CBSE Second Term Exams Free download in PDF for all the students following NCERT Books 2021-22 for their study.

NCERT Solutions 2021-2022 are applicable for CBSE as well as UP Board, MP Board, Gujrat Board students who are following CBSE Syllabus (Curriculum) 2021-2022. Join the Discussion Forum to ask your doubts. Download Class 11 Math UP Board Solutions chapter 12 in PDF format free.## NCERT Solutions for Class 11 Maths Chapter 12

### NCERT Solutions for Class 11 Maths Chapter 12 in PDF

Class: | 11 |

Subject: | Maths |

Chapter 12: | Introduction to Three Dimensional Geometry |

### 11th Maths Chapter 12 Solutions

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry is given below to download in PDF form free for new academic session 2021-2022. Download Offline Apps 2021-22 based on latest NCERT Books and following current CBSE Syllabus 2021-22. Join the Discussion Forum to ask your doubts and reply the questions asked by other users.

#### Important Terms of 3-D Geometry

1. Three mutually perpendicular lines in space define three mutually perpendicular planes, called Coordinate planes, which in turn divide the space into eight parts known as octants and the lines are known as Coordinate axes.

2. Coordinates of a points lying on x-axis, y-axis & z-axis are of the from (x, 0, 0), (0, y, 0), (0, 0, z) respectively.

3. Coordinates of a points lying on xy – plane, yz – plane, and xz – plane are of the from (x, y, 0), (0, y, z), (x, 0, z) respectively.

4. The reflection of the point (x, y, z) in xy – plane yz – plane, and xz plane is (x, y, –z), (–x, y, z), (x,–y, z) respectively.

5. Coordinates of a point P are the perpendicular distances of P from three coordinate planes YZ, ZX and XY respectively.

##### Questions from Exam Papers

1. Find the image of (–5, 4, –3) in xz plane. [Answer: (-5, -4, -3)]

2. Name the octant in which (–5, 4, –3) lies. [Answer: OX’YZ’]

3. Let A, B, C be the feet of perpendiculars from point P on the xy, yz and xz planes respectively. Find the coordinates of A, B, C where the point P is (4, –3, –5). [Answer: (4, –3, 0), (0, –3, –5), (4, 0, –5)]

4. What is the perpendicular distance of the point P(6, 7, 8) from xy plane. [Answer: 8]

5. If the distance between the points (a, 2, 1) and (1, –1, 1) is 5, then find the value (s) of a. [Answer: 5, -3]

###### Questions for Practice

1. What are the coordinates of the vertices of a cube whose edge is 2 unit, one of whose vertices coincides with the origin and the three edges passing through the origin? Coincides with the positive direction of the axes through the origin? [Answer: (2, 0, 0), (2, 2, 0), (0, 2, 0), (0, 2, 2), (0, 0, 2), (2, 0, 2), (0, 0, 0), (2, 2, 2)]

2. If a parallelepiped is formed by planes drawn through the point (5, 8, 10) & (3, 6, 8) parallel to the coordinates planes, then find the length of the diagonal of the parallelepiped. [Answer: 2√3]

3. Find the length of the longest piece of a string that can be stretched straight in a rectangular room whose dimensions are 13, 10 and 8 unit. [Answer: √333]

4. Find the distance of point P(3, –2,1) from z–axis. [Answer: √13]

5. Write coordinates of foot of perpendicular from (3, 7, 9) on x axis y-axis, z-axis. [Answer: (3, 0, 0)]

### Important Questions on 11th Maths Chapter 12

##### A point is on the x-axis. What are its y-coordinates and z-coordinates?

If a point is on the x-axis, then its y-coordinates and z-coordinates are zero.

##### A point is in the XZ-plane. What can you say about its y-coordinate?

If a point is in the XZ plane, then its y-coordinate is zero.

##### Name the octants in which the following points lie: (1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7).

The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive.

Therefore, this point lies in octant I.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively.

Therefore, this point lies in octant IV.

The x-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively.

Therefore, this point lies in octant VIII.

The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively.

Therefore, this point lies in octant V.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively.

Therefore, this point lies in octant VI.

The x-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively.

Therefore, this point lies in octant II.

The x-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively.

Therefore, this point lies in octant III.

The x-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively.

Therefore, this point lies in octant VIII.

##### Does chapter 12 of 11th Maths NCERT Book has any miscellaneous exercise?

Yes, chapter 12 of grade 11th Maths has a miscellaneous exercise. There are four exercises in chapter 12 of class 11th Maths, and the last exercise is the miscellaneous exercise of chapter 12 of grade 11th Maths. Miscellaneous exercise is a little hard exercise compared to other exercises of this chapter.

##### How many sums are there in chapter 12 of class 11th Maths, and which sums are important and can come in the exams?

Chapter 12 of class 11th Maths has four exercises. The first exercise (Ex 12.1) has two examples and 4 questions. In the second exercise (Ex 12.2), there are four examples and 5 questions. The third exercise (Ex 12.3) contains four illustrations and 5 questions. The last (Miscellaneous) Exercise contains three illustrations and 6 questions.

So, there are 33 sums (20 questions and 13 illustrations) in chapter 12 of class 11th Maths. The important illustrations of chapter 12 are 1, 4, 7, 10, 11, and 12. The important questions of this chapter are questions 3, 4 of exercise 12.1, questions 1, 3, 5 of exercise 12.2, questions 4, 5 of exercise 12.3, and questions 1, 2, 3, 4, 5, 6 of miscellaneous exercise.

##### Which books other than NCERT are good to practice extra questions of chapter 12 of class 11th Maths?

NCERT Exemplar, P.K. Garg and R.S. Aggarwal are some books other than NCERT that are good to practice extra questions of chapter 12 of class 11th Maths. These books are really very nice for revision after going through NCERT. The languages of these books are also simple. Students can easily practice extra questions of chapter 12 of class 11th Maths from these books. Students can also see the previous year’s question papers.

##### Which chapter do students revise before starting chapter 12 of 11th standard Maths?

Before starting chapter 12 (Introduction to three-dimensional geometry) of 11th standard Maths, students should revise chapter 7 (Coordinate geometry) of grade 10th Maths. Chapter 7 of class 10th Maths works as a base for chapter 12 of class 11th Maths.

##### Is chapter 12 of class 11th Maths takes less time to practice?

Yes, chapter 12 of grade 11th Maths is short. There are only 20 questions and 13 examples in chapter 12 of class 11th Maths. Students need a maximum of 5 days if they seriously give 1-2 hours per day to this chapter. This time also depends on student’s efficiency, capability, working speed, and many other factors, etc.