Class 11 Maths NCERT Solutions for Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1

Class 11 Maths NCERT Solutions for Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1

Three Dimensional Geometry Exercise 12.1 Solutions

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

Solution

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


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

Solution

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


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) 

Solution

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.


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.

Solution

(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.

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