# 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 CBSE Syllabus for 2022-23. 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 theseÂ NCERT Maths Solutions of Class 11 and practice offline to score more in their exam. By practising these questions, students can build their confidence levels. It helps the students to boost their reasoning skills.

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### NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1

1. A point is on theÂ x-axis. What are itsÂ yÂ coordinate andÂ 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 itsÂ 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, â€“2, 3), (4, â€“2, â€“5), (4, 2, â€“5), (â€“ 4, 2, â€“5), (â€“ 4, 2, 5), (â€“3, â€“1, 6) (2, â€“ 4, â€“7).

Solution:

Here is the table which represents the octants:

 Octants I II III IV V VI VII VIII x + â€“ â€“ + + â€“ â€“ + y + + â€“ â€“ + + â€“ â€“ z + + + + â€“ â€“ â€“ â€“

(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) TheÂ x-axis andÂ 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) TheÂ x-axis andÂ y-axis taken together determine a plane known asÂ XY Plane.

(ii) The coordinates of points in the XY-plane are of the formÂ (x, y, 0).

(iii) Coordinate planes divide the space intoÂ eightÂ 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