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

*According to the CBSE Syllabus 2023-24, this chapter has been renumbered as Chapter 11.

Three exercises are present in the 12th chapter of NCERT Class 11 Maths, which is categorised under the CBSE Syllabus for 2023-24. The answers to the questions given in the first exercise of the 12th chapter are available here. 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 practise offline to score more in their exams. By practising these questions, students can build their confidence levels. It helps them to boost their reasoning skills.

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

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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 the 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 the I octant.

(ii) (4, -2, 3)

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

So, it lies in the IV octant.

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

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

So, it lies in the VIII octant.

(iv) (4, 2, -5)

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

So, it lies in the V octant.

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

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

So, it lies in the VI octant.

(vi) (-4, 2, 5)

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

So, it lies in the II octant.

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

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

So, it lies in the III octant.

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

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

So, it lies in the VIII octant.

4. Fill in the blanks.
(i) The x-axis and y-axis ate taken together to 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 are taken together to 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

Miscellaneous Exercise on Chapter 12 Solutions 6 Questions

Also, explore – NCERT Class 11 Solutions

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