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 Introduction to Three Dimensional Geometry Exercise 12.1

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

Answer

Any point on x-axis is (x 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 (x1, 0, z1) 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.
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