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

If you're looking for NCERT Solutions of Chapter 12 Introduction to Three Dimensional Geometry Exercise 12.1 then you're at right place. Class 11 Maths NCERT Solutions will be useful guide that will increase your efficiency so you can easily solve the questions that come in the examinations. It will surely help you to improve your marks and boost your confidence.

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

**Answer**

Any point on x-axis is (x

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

Any point lying on XZ-plane is (x

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)

The octant in which the given point lie:

(i) (1, 2, 3), XOYZ

(ii) (4, – 2, 3), XOY’Z

(iii) (4, – 2, – 5), XOY’Z’

(iv) (4, 2, – 5), XOYZ’

(v) (– 4, 2, – 5), X’OYZ’

(vi) (– 4, 2, 5), X’OYZ

(vii) (– 3, – 1, 6), X’OY’Z

(viii) (2, – 4, –7), XOY’Z’

4. Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as ...........

(ii) Coordinates of points in XY-plane are of the form ......

(iii) Coordinate planes divide the space into ......... octants.

(i) The x-axis and y-axis together determine a plane known as XY-plane.

(ii) Coordinates of points in XY-plane are of the form (x1, y 1, 0).

(iii) Coordinate planes divides the space into 8 octants.

_{ 1}, 0, 0) i.e y-coordinate and z-coordinate of this point are 0 and 0 respectively.2. A point is in the XZ-plane. What can you say about its y-coordinate?

**Answer**Any point lying on XZ-plane is (x

_{1}, 0, z_{1}) i.e. 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)

**Answer**The octant in which the given point lie:

(i) (1, 2, 3), XOYZ

(ii) (4, – 2, 3), XOY’Z

(iii) (4, – 2, – 5), XOY’Z’

(iv) (4, 2, – 5), XOYZ’

(v) (– 4, 2, – 5), X’OYZ’

(vi) (– 4, 2, 5), X’OYZ

(vii) (– 3, – 1, 6), X’OY’Z

(viii) (2, – 4, –7), XOY’Z’

4. Fill in the blanks:

(i) The x-axis and y-axis taken together determine a plane known as ...........

(ii) Coordinates of points in XY-plane are of the form ......

(iii) Coordinate planes divide the space into ......... octants.

**Answer**(i) The x-axis and y-axis together determine a plane known as XY-plane.

(ii) Coordinates of points in XY-plane are of the form (x1, y 1, 0).

(iii) Coordinate planes divides the space into 8 octants.