# 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 for their study. Applicable for CBSE as well as UP Board, MP Board, Gujrat Board students from 2019-20 onward as their are following CBSE Curriculum 2019-2020. Join the Discussion Forum to ask your doubts.

 Class: 11 Subject: Maths Chapter 12: Introduction to Three Dimensional Geometry

## NCERT Solutions for Class 11 Maths Chapter 12

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### Class 11 Maths Chapter 12 Introduction to 3-D Geometry Sols

#### Important Terms of 3-D Geometry

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

##### Important Extra Questions with Answer
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]
6. 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)]
7. 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]

###### Try These
• 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]
• Find the distance of point P(3, –2,1) from z–axis. [Answer: √13]
• Write coordinates of foot of perpendicular from (3, 7, 9) on x axis y-axis, z-axis. [Answer: (3, 0, 0)]

#### 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.