**NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry** – Here are all the NCERT solutions for Class 11 Maths Chapter 12. This solution contains questions, answers, images, explanations of the complete chapter 12 titled Of Introduction to Three Dimensional Geometry taught in Class 11. If you are a student of Class 11 who is using NCERT Textbook to study Maths, then you must come across chapter 12 Introduction to Three Dimensional Geometry After you have studied lesson, you must be looking for answers of its questions. Here you can get complete NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry in one place.

## NCERT Solutions Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry

Here on **AglaSem Schools**, you can access to **NCERT Book Solutions** in free pdf for Maths for Class 11 so that you can refer them as and when required. The NCERT Solutions to the questions after every unit of NCERT textbooks aimed at helping students solving difficult questions.

For a better understanding of this chapter, you should also see summary of Chapter 12 Introduction to Three Dimensional Geometry , Maths, Class 11.

Class | 11 |

Subject | Maths |

Book | Mathematics |

Chapter Number | 12 |

Chapter Name |
Introduction to Three Dimensional Geometry |

### NCERT Solutions Class 11 Maths chapter 12 Introduction to Three Dimensional Geometry

Class 11, Maths chapter 12, Introduction to Three Dimensional Geometry solutions are given below in PDF format. You can view them online or download PDF file for future use.

### Introduction to Three Dimensional Geometry

**NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry Download**

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### Question & Answer

Q.1:A point is on the x-axis. What are its y-coordinate and z-coordinates?

Ans :It a point Is on the x-axis, then Its "y-coordinates and z-coordinates are zero.

Q.2:A point is in the XZ-plane. What can you say about its y-coordinate?

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

Q.3: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).

Ans :The x-coordinate, y-coordinate, and z-coordinate Of point (I, 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 or 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 Ill. 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.

Q.4:Fill in the blanks: (i) The x-axis and y-axis taken together determine a plane known as_______. (ii) The coordinates of points in the XY-plane are of the form _______. (iii) Coordinate planes divide the space into ______ octants.

Ans :(i) The x-axis and y-axis taken together determine a plane known as XY-plane. (ii) The coordinates of points in the XY-plane are of the form (x, y, 0). (iii) Coordinate planes divide the space into eight octants.

Q.5:Find the distance between the following pairs of points: (i) (2, 3, 5) and (4, 3, 1) (ii) (–3, 7, 2) and (2, 4, –1) (iii) (–1, 3, – 4) and (1, –3, 4) (iv) (2, –1, 3) and (–2, 1, 3).

Ans :(i) The distance between points \(P\left(x_{1,}, y_{1,} z_{1}\right)\) and \(\mathrm{P}\left(\mathrm{x}_{2}, \mathrm{y}_{2,}, \mathrm{z}_{2}\right)\) is given by \(\begin{array}{l}{\mathrm{PQ}=\sqrt{\left(x_{z}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}+\left(z_{2}-z_{1}\right)^{2}}} \\ {\text { (1) Distance between points }(2,3,5) \text { and }(4,3,1)} \\ {=\sqrt{(4-2)^{2}+(3-3)^{2}+(1-5)^{2}}} \\ {=\sqrt{4+16}} \\ {=\sqrt{20}} \\ {=2 \sqrt{5}}\end{array}\) \(\begin{array}{l}{\text { (ii) D Distance between points }(-3,7,2) \text { and }(2,4,-1)} \\ {=\sqrt{(2+3)^{2}+(4-7)^{2}+(-1-2)^{2}}} \\ {=\sqrt{(5)^{2}+(-3)^{2}+(-3)^{2}}} \\ {=\sqrt{25+9+9}} \\ {=\sqrt{43}}\end{array}\) \(\begin{array}{l}{\text { (iii) Distance between points }(-1,3,-4) \text { and }(1,-3,4)} \\ {=\sqrt{(1+1)^{2}+(-3-3)^{2}+(4+4)^{2}}} \\ {=\sqrt{(2)^{2}+(-6)^{3}+(8)^{2}}} \\ {=\sqrt{4+36+64}=\sqrt{104}=2 \sqrt{26}}\end{array}\) (iv) Distance between points (2, -1, 3) and (-2, 1, 3) \(\begin{aligned} &=\sqrt{(-2-2)^{2}+(1+1)^{2}+(3-3)^{2}} \\ &=\sqrt{(-4)^{2}+(2)^{2}+(0)^{2}}+(3-3)^{2} \\ &=\sqrt{16+4} \\ &=\sqrt{20} \\ &=2 \sqrt{5} \end{aligned}\)

## NCERT / CBSE Book for Class 11 Maths

You can download the NCERT Book for Class 11 Maths in PDF format for free. Otherwise you can also buy it easily online.

- Click here for NCERT Book for Class 11 Maths
- Click here to buy NCERT Book for Class 11 Maths

### All NCERT Solutions Class 11

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### All NCERT Solutions

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