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RD Sharma Solution for Class 11 Science Mathematics Chapter 28 - Introduction to 3-D coordinate geometry

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Our RD Sharma Textbook Solutions are considered extremely helpful for solving the tough questions which are asked in the CBSE Class 11 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 28 - Introduction to 3-D coordinate geometry.

All our solutions are created in accordance with the latest CBSE syllabus, and they are amended from time to time to provide the most relevant answers. Our free RD Sharma Solutions for CBSE Class 11 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 11 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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RD Sharma Solution for Class 11 Science Mathematics Chapter 28 - Introduction to 3-D coordinate geometry Page/Excercise 28.1

Solution 1(i)

All are positive, so octant is XOYZ

 

Solution 1(ii)

X is negative and rest are positive, so octant is X'OYZ

Solution 1(iii)

Y is negative and rest are positive, so octant is XOY'Z

Solution 1(iv)

Z is negative and rest are positive, so octant is XOYZ'

Solution 1(v)

X and Y are negative and Z is positive, so octant is X'OY'Z

Solution 1(vi)

All are negative, so octant is X'OY'Z'

Solution 1(vii)

Y and Z are negative, so octant is XOY'Z'

Solution 1(viii)

X and Z are negative, so octant is X'OYZ'

Solution 2(i)

YZ plane is x-axis, so sign of x will be changed. So answer is (2, 3, 4)

Solution 2(ii)

XZ plane is y-axis, so sign of y will be changed. So answer is (-5, -4, -3)

Solution 2(iii)

XY-plane is z-axis, so sign of Z will change. So answer is (5, 2, 7)

Solution 2(iv)

XZ plane is y-axis, so sign of Y will change, So answer is (-5, 0, 3)

Solution 2(v)

XY plane is Z-axis, so sign of Z will change So answer is (-4, 0, 0)

Solution 3

Vertices of cube are

(1, 0, -1) (1, 0, 4) (1, -5, -1)

(1, -5, 4) (-4, 0, -1) (-4, -5, -4)

(-4, -5, -1) (4, 0, 4) (1, 0, 4)

Solution 4

3-(-2)=5, |0-5|=5, |-1-4|=5

5, 5, 5 are lengths of edges

Solution 5

5-3=2, 0-(-2)=2, 5-2=3

2, 2, 3 are lengths of edges

Solution 6

 

 

 

 

Solution 7

(-3, -2, -5) (-3, -2, 5) (3, -2, -5) (-3, 2, -5) (3, 2, 5)

(3, 2, -5) (-3, 2, 5)

RD Sharma Solution for Class 11 Science Mathematics Chapter 28 - Introduction to 3-D coordinate geometry Page/Excercise 28.2

Solution 1

Solution 2

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 4(i)

Solution 4(ii)

Solution 4(iii)

Solution 5

Solution 6

Solution 7

Solution 8

Solution 9

text Let    A end text equals open parentheses 0 comma 7 comma 10 close parentheses text ,  B = end text open parentheses minus 1 comma 6 comma 6 close parentheses text   and end text space C equals open parentheses minus 4 comma 9 comma 6 close parentheses

A B equals square root of left parenthesis 0 plus 1 right parenthesis squared plus left parenthesis 7 minus 6 right parenthesis squared plus left parenthesis 10 minus 6 right parenthesis squared end root
equals square root of left parenthesis 1 right parenthesis squared plus left parenthesis 1 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root
equals square root of 18
equals 3 square root of 2 space space text units end text

B C equals square root of left parenthesis minus 1 plus 4 right parenthesis squared plus left parenthesis 6 minus 9 right parenthesis squared plus left parenthesis 6 minus 6 right parenthesis squared end root
equals square root of left parenthesis 3 right parenthesis squared plus left parenthesis 3 right parenthesis squared plus 0 end root
equals square root of 18
equals 3 square root of 2 space space text units end text

A C equals square root of left parenthesis 0 plus 4 right parenthesis squared plus left parenthesis 7 minus 9 right parenthesis squared plus left parenthesis 10 minus 6 right parenthesis squared end root
equals square root of left parenthesis 4 right parenthesis squared plus left parenthesis minus 2 right parenthesis squared plus left parenthesis 4 right parenthesis squared end root
equals square root of 36
equals 6 space space text units end text

left parenthesis A B right parenthesis squared plus left parenthesis B C right parenthesis squared
equals open parentheses 3 square root of 2 close parentheses squared plus open parentheses 3 square root of 2 close parentheses squared
equals 18 plus 18
equals 36
equals left parenthesis A C right parenthesis squared

text Also   end text l left parenthesis A B right parenthesis equals l left parenthesis B C right parenthesis

text Hence    end text open parentheses 0 comma 7 comma 10 close parentheses text ,  end text open parentheses minus 1 comma 6 comma 6 close parentheses text   and end text space open parentheses minus 4 comma 9 comma 6 close parentheses space text are   the   vertices   of   an   isosceles   right-angled   triangle. end text

Solution 10

Solution 11

Solution 12

Solution 13

Solution 14

Solution 15

Solution 16

Solution 17

Solution 18

Solution 19

Solution 20(i)

Solution 20(ii)

Solution 20(iii)

Solution 21

Solution 22

Solution 23

Solution 24

Solution 20(iv)

  

RD Sharma Solution for Class 11 Science Mathematics Chapter 28 - Introduction to 3-D coordinate geometry Page/Excercise 28.3

Solution 1

  

Solution 2

 

 

 

 

 

 

 

 

 

 

 

Solution 3

 

 

 

 

 

 

 

 

Solution 4

 

 

 

 

 

 

Solution 5

 

 

 

 

 

 

 

 

Solution 6

 

 

 

 

 

 

Solution 7

  

 

 

 

 

 

 

 

 

 

Solution 8

 

 

 

 

 

 

 

 

Solution 9

 

 

 

 

 

 

 

 

 

 

 

 

 

Solution 10

 

 

 

 

 

 

 

 

 

Solution 11

 

 

 

 

 

 

 

 

Solution 12

 

 

 

 

 

 

 

 

 

 

Solution 13

 

 

 

 

 

 

 

Solution 14

 

 

 

 

 

 

 

Solution 15

 

 

 

 

 

 

 

Solution 16

 

 

 

 

 

 

 

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 11. Access the CBSE Class 11 Mathematics Chapter 28 - Introduction to 3-D coordinate geometry for free. The textbook questions have been solved by our subject matter experts to help you understand how to answer them. Our RD Sharma Textbook Solutions will help you to study and revise, and you can easily clear your fundamentals of Chapter 28 - Introduction to 3-D coordinate geometry.

Text Book Solutions

CBSE XI Science - Mathematics

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