by Tiwari Academy
NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry in English and Hindi Medium for CBSE Session 2024-25. The solutions of chapter 11 class 11th mathematics is revised according to new textbooks and rationalised syllabus for academic year 2024-25.
NCERT Solutions for Class 11 Maths Chapter 11 in English Medium
Class 11 Maths Exercise 11.1 in English
Class 11 Maths Exercise 11.2 in English
Class 11 Maths Misc. Exercise 11 in English
NCERT Solutions for Class 11 Maths Chapter 11 in Hindi Medium
Class 11 Maths Exercise 11.1 in Hindi
Class 11 Maths Exercise 11.2 in Hindi
Class 11 Maths Misc. Exercise 11 in Hindi
Related Links
Class 11 Maths NCERT Solutions
Class 11 all Subject NCERT Solutions
NCERT Solutions for Class 11 Maths Chapter 11
NCERT (https://ncert.nic.in/) Solutions are applicable for CBSE as well as UP Board, MP Board, Gujrat Board students who are following CBSE Curriculum 2024-25. Join the Discussion Forum to ask your doubts. Download Class 11 Math UP Board Solutions chapter 11 in PDF format free.
11th Maths Chapter 11 Solutions
NCERT Solutions for Class 11 Maths Chapter 11 Introduction to Three Dimensional Geometry is given below to download free for new academic session. Download Offline Apps 2024-25 based on latest NCERT Books and following current CBSE Board Syllabus.
| Class: 11 | Mathematics |
| Chapter 11: | Introduction to Three Dimensional Geometry |
| Number of Exercises: | Three (2 + Miscellaneous) |
| Content: | Exercises and Extra Questions |
| Mode: | Online Text and Videos Format |
| Academic Year: | CBSE 2024-25 |
| Medium: | Hindi and English Medium |
NCERT Solutions App for 11th Standard
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]
Important Questions on 11th Maths Chapter 11
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.
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)]
Does chapter 11 of 11th Maths NCERT Book has any miscellaneous exercise?
Yes, chapter 11 of grade 11th Maths has a miscellaneous exercise. There are three exercises in chapter 11 of class 11th Maths, and the last exercise is the miscellaneous exercise of chapter 11 of grade 11th Maths. Miscellaneous exercise is a little difficult exercise compared to other exercises of this chapter.
How many sums are there in chapter 11 of class 11th Maths, and which sums are important and can come in the exams?
Chapter 11 of class 11th Maths has four exercises. The first exercise (Ex 11.1) has two examples and 4 questions. In the second exercise (Ex 11.2), there are four examples and 5 questions. The last (Miscellaneous) Exercise contains three illustrations and 6 questions.
So, there are ample sums (questions and illustrations) in chapter 11 of class 11th Maths. The important illustrations of chapter 11 are 1, 4, 7, 10, 11, and 12. The important questions of this chapter are questions 3, 4 of exercise 11.1, questions 1, 3, 5 of exercise 11.2, and questions 1, 2, 3, 4, 5, 6 of miscellaneous exercise.
Which books other than NCERT are good to practice extra questions of chapter 11 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 11 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 11 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 11 of 11th standard Maths?
Before starting chapter 11 (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 11 of class 11th Maths.
Is chapter 11 of class 11th Maths takes less time to practice?
Yes, chapter 11 of grade 11th Maths is short. There are only 20 questions and 13 examples in chapter 11 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.
