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NCERT Solutions for Class 11 Maths Chapter 11 Exercise 11.1 - Introduction to Three Dimensional Geometry
Imagine looking up at a drone flying in the sky; you can’t just describe its position using left or right or forward and backward. You also need to know how high it is. That’s exactly where three-dimensional geometry comes into play! This chapter will introduce you to the basic building blocks of 3D geometry: coordinate axes (x, y, z), the coordinate planes, and the coordinates of a point in space. In this NCERT exercise, you will learn how to represent the position of a point in a three-dimensional system using three perpendicular distances from the respective coordinate planes.
This Story also Contains
- NCERT Solutions Class 11 Maths Chapter 11: Exercise 11.1
- Topics covered in Chapter 11 Introduction to Three-Dimensional Geometry Exercise 11.1
- Class 11 Subject-Wise Solutions
The NCERT Solutions for Chapter 11 Exercise 11.1 are designed in a way that you can connect your existing knowledge of 2D geometry to this exciting new dimension. The clear explanations and simple examples provided in these NCERT Solutions will make it easy to visualize and understand 3D space.
NCERT Solutions Class 11 Maths Chapter 11: Exercise 11.1
Question 1: A point is on the x-axis. What are its y-coordinate and z-coordinates?
Answer:
Any point on the x-axis has a zero y coordinate and zero z coordinate.
Question 2 :A point is in the XZ-plane. What can you say about its y-coordinate?
Answer:
When a point is in the XZ plane, the y coordinate of this point will always be zero.
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: (i) Fill in the blanks: The x-axis and y-axis taken together determine a plane known as ______.
Answer:
The x-axis and y-axis taken together determine a plane known as the XY Plane.
Question 4: (ii) Fill in the blanks: The coordinates of points in the XY-plane are of the form _______.
Answer:
The coordinates of points in the XY-plane are of the form (x, y, 0 ).
Question 4: (iii) Fill in the blanks: Coordinate planes divide the space into ______ octants.
Answer:
Coordinate planes divide the space into eight octants.
Also Read
Topics covered in Chapter 11 Introduction to Three-Dimensional Geometry Exercise 11.1
1. Basics of three-dimensional geometry
2. Coordinate system in 3D space
The position of a point is described using three mutually perpendicular axes in 3D geometry. These are x-axis, y-axis and z-axis that form a 3D Cartesian coordinate system. It helps to represent the exact location of objects in space.
3. Definition of coordinate axes (x, y, z axes)
All three axes intersect at the origin (0,0,0) and are perpendicular to each other.
4. Coordinate planes (XY, YZ, and ZX planes)
Each pair of axes forms a plane. These planes divide space into eight parts called octants.
XY-plane- It is formed by x- and y-axes (z=0)
YZ-plane- It is formed by y- and z-axes (x=0)
ZX-plane- It is formed by z- and x-axes (y=0).
5. Octants in 3D geometry
The three axes that divide 3D space into 8 regions are known as octants.
The first octant (positive x, y, and z) is usually where all coordinates are positive. Other octants have different combinations of positive and negative coordinates.
6. Representation of a point in 3D space using (x, y, z)
A point in space is given by an ordered triple (x, y, z), where,
x = distance along x-axis
y = distance along y-axis
z = distance along z-axis
7. Signs of coordinates in different octants
The signs of x, y, and z change based on which octant the point lies in,
1st Octant = (+,+,+)
2nd Octant = (-,+,+)
3rd Octant = (-,-,+)
4th Octant = (+,-,+)
5th to 8th Octants- These include combinations where the z-coordinate is negative, and the signs of x and y vary.
Also Read
Class 11 Subject-Wise Solutions
Follow the links to get your hands on subject-wise NCERT exercises and exemplar solutions to ace your exam preparation.
NCERT Solutions of Class 11 Subject Wise
| NCERT Solutions for Class 11 Maths |
| NCERT Solutions for Class 11 Physics |
| NCERT Solutions for Class 11 Chemistry |
| NCERT Solutions for Class 11 Biology |
Subject Wise NCERT Exampler Solutions
| NCERT Exemplar Solutions for Class 11 Maths |
| NCERT Exemplar Solutions for Class 11 Physics |
| NCERT Exemplar Solutions for Class 11 Chemistry |
| NCERT Exemplar Solutions for Class 11 Biology |
Frequently Asked Questions (FAQs)
Q: Find the distance between two points A (0, 0, 0), B (1, 0, 2),
A:
The distance AB = $((1-0)^2 + (0-0)^2 + (2-0)^2)^(1/2)$
AB = $(5)^(1/2)$
Q: What is the definition of coordinate axes ?
A:
We need two intersecting mutually perpendicular lines in the plane to locate any point in the plane. These perpendicular lines are called the coordinate axes.
Q: What is the octants in three dimensional geometry ?
A:
The coordinate planes in the three-dimensional geometry divide the space into eight parts which are called the octants.
Q: Find the number of octants in the coordinates space ?
A:
Coordinate planes divide the space into eight octants.
Q: Find the octant in which the points (–1,3,5) lies ?
A:
The point (–1,3,5) lies in the second octant.
Q: Find the octant in which the points lies ?
A:
The point (–5,3,– 2) lies in the octant VI.
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