Gujarat Board GSEB Textbook Solutions Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Textbook Questions and Answers.

## Gujarat Board Textbook Solutions Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1

Question 1.

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

Solution:

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.

Question 2.

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

Solution:

Any point lying on xz-plane is (x_{1}, 0, z_{1}), i.e., Its y-coordinate is zero.

Question 3.

Name the octant 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:

The octants in which the given points lie.

(i) (1, 2, 3) : I

(ii) (4, – 2, 3) : IV

(iii) (4, – 2, – 5) : VIII

(iv) (4, 2, – 5) : V

(v) (- 4, 2, – 5) : VIX

(vi) (- 4, 2, 5) : IIX

(vii) (- 3, – 1, 6) : IIIX

(viii) (2, – 4, – 7) : VIII

4. Fill in the blanks:

- The x-axis and y-axis taken together determine a plane known as …………………..
- Coordinates of points in XY-plane are of the form ………………………
- Coordinate planes divide the space into ……………………… octants

Solution:

- The x-axis and y-axis together determine a plane known as XY-plane.
- Coordinates of points in XY-plane are of the form (x
_{1}, y_{1}, 0). - Coordinate planes divides the space into 8 octants.