# NCERT Solutions for Class 11 Maths Chapter 12

NCERT Solutions for Class 11 Maths Chapter 12 Introduction to Three Dimensional Geometry त्रिविमीय ज्यामिति का परिचय, Free download in PDF for all the students following NCERT Books 2020-21 for their study.

NCERT Solutions 2020-2021 are applicable for CBSE as well as UP Board, MP Board, Gujrat Board students who are following CBSE Syllabus (Curriculum) 2020-2021. 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

 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 2020-2021. Download Offline Apps 2020-21 based on latest NCERT Books and following current CBSE Syllabus 2020-21. Join the Discussion Forum to ask your doubts and reply the questions asked by other users.

• ### 11th Maths Chapter 12 Solutions in PDF

#### 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.