Chapter 12 – Introduction to Three Dimensional Geometry (Ex – 12.1)

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 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 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) XY-plane
(ii) (x, y, 0)
(iii) Eight