Punjab State Board PSEB 11th Class Maths Book Solutions Chapter 12 Introduction to Three Dimensional Geometry Ex 12.1 Textbook Exercise Questions and Answers.
PSEB Solutions for 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 – coordinates and z – coordinates?
Answer.
Coordinates of any point on the X-axis is (x, 0, 0).
Because at X-axis, both y and z – coordinates are zero.
So, its y and z – coordinates are zero.
Question 2.
A point is in the XZ – plane. What can you say about its y-coordinate?
Answer.
Any point on the XZ – plane will have the coordinate (x, 0, z), so its y – coordinate is 0.
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).
Answer.
The x-coordinate, y-coordinate, and z-coordinate of point (1, 2, 3) are all positive. Therefore, this point lies in octant I.
The x-coordinate, y-coordinate, and z-coordinate of point (4, – 2, 3) are positive, negative, and positive respectively. Therefore, this point lies in octant IV.
The x-coordinate, y-coordinate, and z-coordinate of point (4, – 2, – 5) are positive, negative, and negative respectively. Therefore, this point lies in octant VIII.
The x-coordinate, y-coordinate, and z-coordinate of point (4, 2, – 5) are positive, positive, and negative respectively. Therefore, this point lies in octant V.
The x-coordinate, y-coordinate, and z-coordinate of point (- 4, 2, – 5) are negative, positive, and negative respectively. Therefore, this point lies in octant VI.
The x-coordinate, y-coordinate, and z-coordinate of point (- 4, 2, 5) are negative, positive, and positive respectively. Therefore, this point lies in octant II.
The x-coordinate, y-coordinate, and z-coordinate of point ( – 3, – 1, 6) are negative, negative, and positive respectively. Therefore, this point lies in octant III.
The x-coordinate, y-coordinate, and z-coordinate of point (2, – 4, – 7) are positive, negative, and negative respectively. Therefore, this point 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.
Answer.
(i) XY plane
(ii) (x, y, 0)
(iii) eight