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:

The coordinates of any point on the x-axis will be (x, 0, 0). Thus y-coordinate and z-coordinate of the point are zero.

Question 2.

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

Solution:

The coordinates of any point in the XZ-plane will be (x, 0, z). Thus y-coordinate of the point is zero.

Question 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:

Point (1, 2, 3) lies in Octant I.

Point (4, -2, 3) lies in Octant IV.

Point (4, -2, -5) lies in Octant VIII.

Point (4, 2, -5) lies in Octant V.

Point (- 4, 2, -5) lies in Octant VI.

Point (- 4, 2, 5) lies in Octant II.

Point (- 3, -1, 6) lies in Octant III.

Point (2, – 4, -7) lies in Octant VIII.

Question 4.

Fill in the blanks:

(i) The x-axis and y-axis is 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) XY-plane

(ii) (x, y, 0)

(iii) Eight