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

Three exercises are present in the 12th chapter of NCERT Class 11 Maths which is categorized under the term – II CBSE Syllabus for 2021-22. The answers for the questions present in the first exercise of the 12th chapter is available here. The Exercise 12.1 of NCERT Solutions for Class 11 Maths Chapter 12- Introduction to Three Dimensional Geometry is based on the following topics:

1. Introduction to Three Dimensional Geometry
2. Coordinate Axes and Coordinate Planes in Three Dimensional Space
3. Coordinates of a Point in Space

Students can download these NCERT Maths Solutions of Class 11 and practice offline to score more in their second term exam. By practising these questions, students can build their confidence levels. It helps the students to boost their reasoning skills.

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

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

Solution:

If a point is on the x-axis, then the coordinates of y and z are 0.

So the point is (x, 0, 0).

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

Solution:

If a point is in XZ plane, then its y-co-ordinate is 0.

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:

Here is the table which represents the octants:

 Octants I II III IV V VI VII VIII x + – – + + – – + y + + – – + + – – z + + + + – – – –

(i) (1, 2, 3)

Here x is positive, y is positive and z is positive.

So it lies in I octant.

(ii) (4, -2, 3)

Here x is positive, y is negative and z is positive.

So it lies in IV octant.

(iii) (4, -2, -5)

Here x is positive, y is negative and z is negative.

So it lies in VIII octant.

(iv) (4, 2, -5)

Here x is positive, y is positive and z is negative.

So it lies in V octant.

(v) (-4, 2, -5)

Here x is negative, y is positive and z is negative.

So it lies in VI octant.

(vi) (-4, 2, 5)

Here x is negative, y is positive and z is positive.

So it lies in II octant.

(vii) (-3, -1, 6)

Here x is negative, y is negative and z is positive.

So it lies in III octant.

(viii) (2, -4, -7)

Here x is positive, y is negative and z is negative.

So it lies in VIII octant.

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.

### Access Other Exercise Solutions of Class 11 Maths Chapter 12- Introduction to Three Dimensional Geometry

Exercise 12.2 Solutions 5 Questions

Exercise 12.3 Solutions 5 Questions