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RD Sharma Solution for Class 12 Science Mathematics Chapter 26 - Scalar Triple Product

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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 12 exam. TopperLearning Textbook Solutions are compiled by subject experts. Herein, you can find all the answers to the textbook questions for Chapter 26 - Scalar Triple Product.

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 12 Mathematics will strengthen your fundamentals in Mathematics and will help you in your attempts to score more marks in the final examination. CBSE Class 12 students can refer to our solutions any time — while doing their homework and while preparing for the exam.

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Exercise/Page

RD Sharma Solution for Class 12 Science Mathematics Chapter 26 - Scalar Triple Product Page/Excercise 26.1

Solution 1(i)

Solution 1(ii)

Solution 2(i)

Solution 2(ii)

Solution 3(i)

Solution 3(ii)

Solution 3(iii)

Solution 3(iv)

Solution 4(i)

Solution 4(ii)

Solution 4(iii)

Solution 5(i)

Solution 5(ii)

Solution 5(iii)

Solution 5(iv)

Solution 6

Solution 7

A B equals p o s i t i o n space v e c t o r space o f space B minus p o s i t i o n space v e c t o r space o f space A
space space space space space equals 4 i with hat on top minus 2 j with hat on top minus 2 k with hat on top
A C equals p o s i t i o n space v e c t o r space o f space C minus p o s i t i o n space v e c t o r space o f space A
space space space space space equals minus 2 i with hat on top plus 4 j with hat on top minus 2 k with hat on top
A D equals p o s i t i o n space v e c t o r space o f space D minus p o s i t i o n space v e c t o r space o f space A
space space space space space equals minus 2 i with hat on top minus 2 j with hat on top plus 4 k with hat on top
T h e space f o u r space p o i n t s space a r e space c o minus p l a n a r space i f space t h e space v e c t o r s space a r e space c o minus p l a n a r.
T h u s comma space open vertical bar table row 4 cell minus 2 end cell cell minus 2 end cell row cell minus 2 end cell 4 cell minus 2 end cell row cell minus 2 end cell cell minus 2 end cell 4 end table close vertical bar equals 4 open square brackets 16 minus 4 close square brackets plus 2 open square brackets minus 8 minus 4 close square brackets minus 2 open square brackets 4 plus 8 close square brackets equals 48 minus 24 minus 24 equals 0
H e n c e space p r o v e d.

Solution 8

L e t space O A equals 6 i with hat on top minus 7 j with hat on top comma space O B equals 16 i with hat on top minus 19 j with hat on top minus 4 k with hat on top comma space O C equals 3 i with hat on top minus 6 k with hat on top comma space O D equals 2 i with hat on top minus 5 j with hat on top plus 10 k with hat on top
T h u s comma
A B equals O B minus O A equals 10 i with hat on top minus 12 j with hat on top minus 4 k with hat on top
A C equals O C minus O A equals minus 3 i with hat on top plus 7 j with hat on top minus 6 k with hat on top
A D equals O D minus O A equals minus 4 i with hat on top plus 2 j with hat on top plus 10 k with hat on top
T h e space f o u r space p o i n t s space a r e space c o minus p l a n a r space i f space v e c t o r s space A B comma space A C space a n d space A D space a r e space c o minus p l a n a r.
T h u s comma space w e space h a v e
open vertical bar table row 10 cell minus 12 end cell cell minus 4 end cell row cell minus 3 end cell 7 cell minus 6 end cell row cell minus 4 end cell 2 10 end table close vertical bar equals 10 open parentheses 70 plus 12 close parentheses plus 12 open parentheses minus 30 minus 24 close parentheses minus 4 open parentheses minus 6 plus 28 close parentheses equals 820 minus 648 minus 88

Solution 9

Solution 10

Solution 11

Solution 12(i)

Solution 12(ii)

begin mathsize 12px style table attributes columnalign left end attributes row cell straight a with rightwards arrow on top text  =  end text straight i with hat on top text + end text straight j with hat on top text + end text straight k with hat on top text ,  end text straight b with rightwards arrow on top text  =  end text straight i with hat on top text   and   end text stack text c end text with rightwards arrow on top text  =  end text straight c subscript 1 straight i with hat on top text + end text straight c subscript 2 straight j with hat on top text + end text straight c subscript 3 straight k with hat on top text. end text end cell row cell straight c subscript text 2 end text end subscript text  = - 1   and   end text straight c subscript text 3 end text end subscript equals 1 comma end cell row cell text If   end text straight a with rightwards arrow on top comma straight b with rightwards arrow on top comma text    and   end text stack text c end text with rightwards arrow on top text   are   coplanar ,  then   their   scalar   triple   product   is   zero. end text end cell row cell left square bracket table row cell straight a with rightwards arrow on top end cell cell straight b with rightwards arrow on top end cell cell stack text c end text with rightwards arrow on top end cell end table right square bracket equals vertical line table row 1 1 1 row 1 0 0 row cell straight c subscript 1 end cell cell straight c subscript 2 end cell cell straight c subscript 3 end cell end table vertical line equals 0 end cell row cell rightwards double arrow negative straight c subscript 3 plus straight c subscript 2 equals 0 end cell row cell rightwards double arrow straight c subscript 2 equals straight c subscript 3 end cell row cell text But   this   is   a   contradiction   as   it   is   given   that   end text straight c subscript text 2 end text end subscript text  = - 1   and   end text straight c subscript text 3 end text end subscript equals 1. end cell row cell text Hence ,  no   value   of   end text straight c subscript 1 text   can   make   the   vectors   coplanar. end text end cell end table end style

Solution 13

RD Sharma Solution for Class 12 Science Mathematics Chapter 26 - Scalar Triple Product Page/Excercise MCQ

Solution 1

Correct option: (a)

  

Solution 2

Correct option: (a)

  

Solution 3

Correct option: (a)

  

Solution 4

Correct option: (c)

  

Solution 5

Correct option: (d)

  

Solution 6

Correct option:(a)

  

Solution 7

Correct option: (c)

  

Solution 8

 

NOTE: Answer not matching with back answer.

Solution 9

Correct option: (a)

  

 

Solution 10

Correct option: (a)

  

Solution 11

Correct option: (d)

 

NOTE: Answer not matching with back answer.

 

Solution 12

Correct option: (c)

  

Solution 13

Correct option: (d)

  

 

Solution 14

Correct option: (d)

 

NOTE: Answer not matching with back answer.

Solution 15

Correct option: (c)

  

RD Sharma Solution for Class 12 Science Mathematics Chapter 26 - Scalar Triple Product Page/Excercise 26VSAQ

Solution 1

Solution 2

Solution 3

Solution 4

Solution 5

Thus, volume of the parallelopiped is straight pi cubic units.

Solution 6

F o r space a n y space v e c t o r space r with rightwards arrow on top comma space w e space h a v e
r with rightwards arrow on top equals open parentheses stack r. with rightwards arrow on top i with overparenthesis on top close parentheses i with overparenthesis on top plus open parentheses stack r. with rightwards arrow on top j with overparenthesis on top close parentheses j with overparenthesis on top plus open parentheses stack r. with rightwards arrow on top k with overparenthesis on top close parentheses k with overparenthesis on top
R e p l a c i n g space r with rightwards arrow on top space b y space a with rightwards arrow on top cross times b with rightwards arrow on top comma space w e space h a v e
a with rightwards arrow on top cross times b with rightwards arrow on top equals open vertical bar open parentheses a with rightwards arrow on top cross times b with rightwards arrow on top close parentheses times i with overparenthesis on top close vertical bar i with overparenthesis on top plus open vertical bar open parentheses a with rightwards arrow on top cross times b with rightwards arrow on top close parentheses times j with overparenthesis on top close vertical bar j with overparenthesis on top plus open vertical bar open parentheses a with rightwards arrow on top cross times b with rightwards arrow on top close parentheses times k with overparenthesis on top close vertical bar k with overparenthesis on top
rightwards double arrow a with rightwards arrow on top cross times b with rightwards arrow on top equals open square brackets a with rightwards arrow on top space b with rightwards arrow on top space i with overparenthesis on top close square brackets i with overparenthesis on top plus open square brackets a with rightwards arrow on top space b with rightwards arrow on top space j with overparenthesis on top close square brackets j with overparenthesis on top plus open square brackets a with rightwards arrow on top space b with rightwards arrow on top space k with overparenthesis on top close square brackets k with overparenthesis on top

Solution 7

Solution 8

Solution 9

Solution 10

Solution 11

begin mathsize 12px style table attributes columnalign left end attributes row cell a with rightwards arrow on top equals 2 i with hat on top plus j with hat on top plus 3 k with hat on top comma b with rightwards arrow on top equals negative i with hat on top plus 2 j with hat on top plus k with hat on top text   and   end text c with rightwards arrow on top equals 3 i with hat on top plus j with hat on top plus 2 k with hat on top end cell row cell b with rightwards arrow on top cross times c with rightwards arrow on top equals vertical line table row cell i with hat on top end cell cell j with hat on top end cell cell k with hat on top end cell row cell negative 1 end cell 2 1 row 3 1 2 end table vertical line equals i with hat on top left parenthesis 4 minus 1 right parenthesis minus j with hat on top left parenthesis negative 5 right parenthesis plus k with hat on top left parenthesis negative 1 minus 6 right parenthesis end cell row cell equals 3 i with hat on top plus 5 j with hat on top minus 7 k with hat on top end cell row cell a with rightwards arrow on top. left parenthesis b with rightwards arrow on top cross times c with rightwards arrow on top right parenthesis equals left parenthesis 2 i with hat on top plus j with hat on top plus 3 k with hat on top right parenthesis. left parenthesis 3 i with hat on top plus 5 j with hat on top minus 7 k with hat on top right parenthesis end cell row cell equals 6 plus 5 minus 21 equals negative 10 end cell end table end style

TopperLearning provides step-by-step solutions for each question in each chapter in the RD Sharma textbook for class 9. Access the CBSE Class 9 Mathematics Chapter 26 - Scalar Triple Product 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 26 - Scalar Triple Product.

Text Book Solutions

CBSE XII Science - Mathematics

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