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.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | Aakash | Unacademy

Suggested: JEE Main: high scoring chapters | Past 10 year's papers

This Story also Contains

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.

Also see-

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook

NCERT Solutions of Class 11 Subject Wise

Subject Wise NCERT Exampler Solutions

Happy learning!!!

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.

Also Read

NCERT Class 11 Chemistry Chapter 4 Notes Chemical Bonding and Molecular Structure - Download PDF

Hydrogen Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 9 Notes - Download PDF

The S-Block Elements Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 10 Notes - Download PDF

The P-Block Elements Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 11 Notes - Download PDF

Environmental Chemistry Class 11th Notes - Free NCERT Class 11 Chemistry Chapter 14 Notes - Download PDF

NCERT Class 11 Chemistry Chapter 3 Notes - Download PDF

NCERT Solutions for Class 11 Physics Chapter 6 Work Energy and Power

NCERT Solutions for Class 11 Chemistry Chapter 5 States of Matter

NCERT Class 11 Physics Chapter 5 Notes Laws of Motion - Download PDF

NCERT Class 11 Physics Chapter 3 Notes Motion in a straight Line - Download PDF

NCERT Solutions for Exercise 10.1 Class 11 Maths Chapter 10 - Straight Lines

NCERT Solutions for Miscellaneous Exercise Chapter 16 Class 11 - Probability

NCERT Exemplar Class 11 Maths Solutions Chapter 12 Introduction to Three Dimensional Geometry

NCERT Exemplar Class 11 Maths Solutions Chapter 10 Straight Lines

NCERT Exemplar Class 11 Maths Solutions Chapter 6 Linear Inequalities

NCERT Exemplar Class 11 Maths Solutions Chapter 16 Probability

NCERT Exemplar Class 11 Maths Solutions Chapter 14 Mathematical Reasoning

NCERT Exemplar Class 11 Maths Solutions Chapter 7 Permutations and Combinations

Articles

MVPP Scholarship Exam 2024: Mukhyamantri Vigyan Pratibha Pariksha Registration, Exam Date

Dec 16, 2024

Silverzone ISSO Answer Key 2024-25: Download PDF

Dec 16, 2024

Silverzone IOEL Answer Key 2024 – Download International Olympiad of English Language Solutions

Dec 16, 2024

Silverzone Olympiad IOM Answer Key 2024-25: Qualifying Marks, Score

Dec 16, 2024

Silverzone STEM Olympiad Answer Key 2024-25: Check Answer Key for all Classes

Dec 16, 2024

Silverzone ABHO Answer Key 2024 | Download Akhil Bhartiya Hindi Olympiad Solutions

Dec 16, 2024

Silverzone SKGKO Answer Key 2024-25: Download Smart Kid GK Olympiad Answer Key @ silverzone.org

Dec 16, 2024

IGNOU BEd Answer Key 2025: Download OMR Sheet Here

Dec 13, 2024

Upcoming School Exams

National Institute of Open Schooling 10th examination

Application Date:21 November,2024 - 20 December,2024

Application Process

Exam Pattern

Mock Test

National Institute of Open Schooling 12th Examination

Application Date:21 November,2024 - 20 December,2024

Application Process

Exam Pattern

Admit Card

National Means Cum-Merit Scholarship

Admit Card Date:27 November,2024 - 22 December,2024

Eligibility Criteria

Application Process

Exam Pattern

West Bengal Board 12th Examination

Exam Date:02 December,2024 - 20 December,2024

Result

Exam Pattern

Admit Card

Gujarat Board Secondary School Certificate Examination

Late Fee Application Date:11 December,2024 - 20 December,2024

Exam Pattern

Admit Card

Result

View All School Exams

Get answers from students and experts

Popular Questions

A block of mass 0.50 kg is moving with a speed of 2.00 ms^-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

Option 1) $0.34\; J$	Option 2) $0.16\; J$
Option 3) $1.00\; J$	Option 4) $0.67\; J$

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up ? Fat supplies 3.8×10⁷J of energy per kg which is converted to mechanical energy with a 20% efficiency rate. Take g = 9.8 ms⁻² :

Option 1)

2.45×10⁻³ kg

Option 2)

6.45×10⁻³ kg

Option 3)

9.89×10⁻³ kg

Option 4)

12.89×10⁻³ kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

Option 1) $2,000 \; J - 5,000\; J$	Option 2) $200 \, \, J - 500 \, \, J$
Option 3) $2\times 10^{5}J-3\times 10^{5}J$	Option 4) $20,000 \, \, J - 50,000 \, \, J$

A particle is projected at 60⁰ to the horizontal with a kinetic energy $K$ . The kinetic energy at the highest point

Option 1) $K/2\,$	Option 2) $\; K\;$
Option 3) $zero\;$	Option 4) $K/4$

In the reaction,

$2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}$

Option 1) $11.2\, L\, H_{2(g)}$ at STP is produced for every mole $HCL_{(aq)}$ consumed	Option 2) $6L\, HCl_{(aq)}$ is consumed for ever $3L\, H_{2(g)}$ produced
Option 3) $33.6 L\, H_{2(g)}$ is produced regardless of temperature and pressure for every mole Al that reacts	Option 4) $67.2\, L\, H_{2(g)}$ at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, $Mg_{3}(PO_{4})_{2}$ will contain 0.25 mole of oxygen atoms?

Option 1) 0.02	Option 2) 3.125 × 10^-2
Option 3) 1.25 × 10^-2	Option 4) 2.5 × 10^-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

Option 1) decrease twice	Option 2) increase two fold
Option 3) remain unchanged	Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

Option 1) Molality	Option 2) Weight fraction of solute
Option 3) Fraction of solute present in water	Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol^-1) is

Option 1) twice that in 60 g carbon	Option 2) 6.023 × 10²²
Option 3) half that in 8 g He	Option 4) 558.5 × 6.023 × 10²³

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t²) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m² , the number of rotations made by the pulley before its direction of motion if reversed, is