RBSE Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1

Rajasthan Board RBSE Solutions for Class 11 Maths Chapter 12 Introduction to three Dimensional Geometry Ex 12.1 Textbook Exercise Questions and Answers.

RBSE Class 11 Maths Solutions 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 ^-coordinate?
Answer:
Given that, point lie on x-axis. Thus, its coordinate will be (x, 0, 0).
This point lies on x-axis, y-coordinate = 0 and z-coordinate = 0

Question 2.
A point is in the XZ-plane. What can you say about its y-coordinate?
Answer:
Given that, point lie in XZ-plane and coordinates of point lie in XZ-plane = (x, 0, z)
Thus, y-coordinate of any point lie in XZ-plane = 0

Question 3.
Name the octants in which the following point 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:
In point (1, 2, 3) x = 1, y = 2, z = 3. All three are positive.
Thus, point (1, 2, 3) lie in 1st octant.
In point (4, -2, 3), x = 4, y = - 2, z = 3
Here, x coordinate is positive, y-coordinate is negative and z-coordinate is positive.
Thus, point (4, - 2, 3) lie in 4th octant.
Since, in two dimensional system, point (4, - 2) lie in 4th quadrant and in (4, - 2, 3) z-coordinate is positive in point (4, - 2, - 5), x = 4, y = - 2, z = - 5
Here, x coordinate is positive and y coordinate is negative and z coordinate is also negative.
Thus, point (4, -2, - 5) will lie in 8^th octant.
Since, in two dimensional system point (4, - 2) lie in 4th quadrant and in point (4, -2, -5) z-coordinate is negative. Thus, it will lie in (4 + 4) = 8 i.e. 8^th octant.
In point (4, 2, - 5). x = 4, y = 2, z = - 5
Here, x-coordinate is positive, y -coordinate is positive and z-coordinate is negative.
Thus, point (4, 2, -5) will lie in V^th octant.
Since, in two dimensional System point (4, 2) lie in 1st quadrant and in point (4, 2, -5) z-coordinate is negative. Thus, point (4, 2, -5) will lie in (1 + 4) = 5 i.e. 5^th octant.
In point (-4, 2, -5), x = - 4, y = 2, z = -5
Here, x coordinate is negative, y-coordinate is positive and
z-coordinate is negative. It will lie in 6^th octant.
Since, in two dimensional system, point (- 4, 2) lie in 2nd quadrant and in point (- 4, 2, - 5) z-coordinate is negative, thus it will lie in (2 + 4) = 6 or 6^th octant.
In point (- 4, 2, 5), x = - 4, y = 2, z = 5 z-coordinate is negative. Thus, it will lie in (2 + 4) = 6 or 6th octant.
In point (- 4, 2, 5), x = - 4, y = 2, z = 5
Here, x-coordinate is negative, y-coordinate is positive and z-coordinate is positive. Point will lie in 2nd octant. Since in two dimensional system point (- 4, 2) lie in 2nd quadrant and in (- 4, 2, 5), z-coordinate is positive.
Thus, (- 4, 2, 5) will lie in 2nd octant.
In point (- 3, -1, 6), x = - 3, y = -1, z = 6
Here, x-coordinate is negative, y-coordinate is negative and z-coordinate is positive. Point (-3, -1, 6) will lie in 3rd octant.
Since, in two dimensional system, point (- 3, -1) lie in 3^rd quadrant and in (- 3, -1, 6), z-coordinate is positive. Thus, (- 3, -1, 6) will lie in 3rd octant.
In point (2, - 4, - 7), x = 2, y = - 4, z = - 7 Here, x-coordinate is positive, y-coordinate is negative and z-coordinate is negative. Point (2, - 4, -7) will lie in 8^th octant.
Since, in two dimensional system, point (2, - 4) lie in 4th quadrant and in point (2, - 4, - 7), z-coordinate is negative. Thus, it will lie in (4 + 4) = 8 or 8^th octant.
Now, we will find location of (2, -4, -7) in two dimensional system. In two dimensional system point is (2, - 4) which lie in 4^th quadrant.
z-coordinate of point is negative
Thus, it will lie in (4 + 4) = 8 i.e. 8th octant

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 AT plane are of the form .................... .
(iii) Coordinate planes divide the space into .................... . octants.
Answer:
(i) XY -plane
(ii) (x, y, 0)
(iii) 8