## NCERT Solutions for Class 11 Maths Chapter 12 – Introduction to Three Dimensional Geometry Ex 12.1

#### Page No 271:

#### Question 1:

A point is on the

*x*-axis. What are its*y*-coordinates and*z*-coordinates?#### Answer:

If a point is on the

*x*-axis, then its*y*-coordinates and*z*-coordinates are zero.#### Question 2:

A point is in the XZ-plane. What can you say about its

*y*-coordinate?#### Answer:

If a point is in the XZ plane, then its

*y*-coordinate is zero.#### Question 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)

#### Answer:

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**.#### Question 4:

Fill in the blanks:

#### Answer:

(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.

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