NCERT Solutions For Class 11 Maths chapter-12 Introduction to Three Dimensional Geometry Exercise 12.1

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

NCERT Solutions for Class 11 Maths Chapter-11 Conic Sections Exercise 12.1 is prepared by the expert of Physics Wallah score more with Physics Wallah NCERT Class 11 maths solutions. You can download and share NCERT Solutions for Class 11 Maths.

NCERT Solutions for Class-11 Maths Exercise 12.1

In each of the following Exercises 1 to 4, find the equations :

Question1. 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.

Question2. A point is in the X Z-plane. What can you say about its y-coordinate?

Solution :
If a point is in the X Z plane, then its y-coordinate is zero.

Question3. 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 :
Thex-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.

Thex-coordinate, y-coordinate, and z-coordinate of point (4, –2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.

Thex-coordinate, y-coordinate, and z-coordinate of point (4, –2, –5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

Thex-coordinate, y-coordinate, and z-coordinate of point (4, 2, –5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.

Thex-coordinate, y-coordinate, and z-coordinate of point (–4, 2, –5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.

Thex-coordinate, y-coordinate, and z-coordinate of point (–4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.

Thex-coordinate, y-coordinate, and z-coordinate of point (–3, –1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.

Thex-coordinate, y-coordinate, and z-coordinate of point (2, –4, –7) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.

Question4. 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.