NCERT Solutions for Exercise 12.1 Class 11 Maths Chapter 12 - Introduction to Three Dimensional Geometry

Edited By Ravindra Pindel | Updated on Jul 12, 2022 04:50 PM IST

In the previous classes, you have already learned about two-dimensional geometry. You also know about the location of a point in the plane and different types of curves like line, parabola, circle, hyperbola, ellipse, etc. In a real-life scenario, you have to deal with the point located in three-dimensional geometry. NCERT solutions for Class 11 Maths chapter 12 exercise 12.1 consists of questions related to coordinates of points in space. You can relate the concepts of three-dimensional geometry with two-dimensional geometry. If you are good with two-dimensional geometry concepts it won't take much effort from you to get command on the Class 11th Maths chapter 12 exercise 12.1.

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Introduction To Three Dimensional Geometry Class 11th Chapter 12 Exercise: 12.1
Question:1 A point is on the x-axis. What are its y-coordinate and z-coordinates?
More About NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1:-
Benefits of NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1:-
NCERT Solutions of Class 11 Subject Wise
Subject Wise NCERT Exampler Solutions

In two-dimensional geometry, two numbers were used to represent the perpendicular distance of a point from two axes but in three-dimensional geometry, three numbers are representing the perpendicular distances of the point from three mutually perpendicular planes. These three numbers representing the three distances from the planes are called the coordinates of the point. You will about coordinates of the point, coordinate axes, and coordinate planes in three-dimensional space in the exercise 12.1 Class 11 Maths. You can click on the line NCERT Solutions if you are looking for NCERT solutions at one place.

Also, see

Three Dimensional Geometry Exercise 12.2

Three Dimensional Geometry Exercise 12.3

Three Dimensional Geometry Miscellaneous Exercise

Introduction To Three Dimensional Geometry Class 11th Chapter 12 Exercise: 12.1

Question:1 A point is on the x-axis. What are its y-coordinate and z-coordinates?

Answer:

Any point on x-axis have 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 XZ plane, the y coordinate of this point will always be 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).

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 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.

Benefits of NCERT Solutions for Class 11 Maths Chapter 12 Exercise 12.1:-

Class 11 Maths chapter 12 exercise 12.1 solutions are designed by subject matter experts on the basis of guidance given by CBSE, so you can easily upon them.
Class 11 Maths chapter 12 exercise 12.1 are very useful in solving some real-life problems like finding coordinates of planes in space.
You can Class 11th Maths chapter 12 exercise 12.1 solutions for reference while solving the problem from this exercise.

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NCERT Solutions of Class 11 Subject Wise

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Frequently Asked Questions (FAQs)

1. What is the definition of coordinate axes ?

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.

2. What is the octants in three dimensional geometry ?

The coordinate planes in the three-dimensional geometry divide the space into eight parts which are called the octants.

3. Find the distance between two points A (0, 0, 0), B (1, 0, 2),

The distance AB = ((1-0)^2 + (0-0)^2 + (2-0)^2)^(1/2)

AB = (5)^(1/2)

4. Find the number of octants in the coordinates space ?

Coordinate planes divide the space into eight octants.

5. Find the octant in which the points (–1,3,5) lies ?

The point (–1,3,5) lies in the second octant.

6. Find the octant in which the points lies ?

The point (–5,3,– 2) lies in the octant VI.

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