Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • How to solve this problem- - Vector Algebra - JEE Main-2

If  \vec{a},\vec{b},\vec{c} are non­-coplanar vector and \; \lambda is a real number then \left [ \lambda\, (\, \vec{a}+\vec{b}\, )\; \lambda ^{2}\, \vec{b}\, \lambda \, \vec{c}\, \right ]=\left [ \vec{a}\; \; \vec{b}+\vec{c}\; \; \vec{b}\; \right ]   for

 

  • Option 1)

    no value of \lambda

  • Option 2)

    exactly one value of \lambda

  • Option 3)

    exactly two values of \lambda

  • Option 4)

    exactly three values of \lambda

 

Answers (1)

best_answer

As we have learned

Scalar Triple Product -

\left [ \vec{a}\;\vec{b}\; \vec{c} \right ]

=\left (\vec{a}\times \vec{b}\right)\cdot \vec{c}= \vec{a}\cdot \left ( \vec{b} \times \vec{c}\right )

=\left (\vec{b}\times \vec{c}\right)\cdot \vec{a}= \vec{b}\cdot \left ( \vec{c} \times \vec{a}\right )

=\left (\vec{c}\times \vec{a}\right)\cdot \vec{b}= \vec{c}\cdot \left ( \vec{a} \times \vec{b}\right )

- wherein

Scalar Triple Product of three vectors \hat{a},\hat{b},\hat{c}.

 

 

Properties of Scalar Triple Product -

\left [K \vec{a} \vec{b} \vec{c} \right ]=K\left [ \vec{a} \vec{b} \vec{c} \right ]

- wherein

\vec{a}, \vec{b} and \vec{c} are the three vectors.

 

 

Properties of Scalar Triple Product -

\left [ \left ( \vec{a}+\vec{b} \right )\vec{c}\; \vec{d} \right ]= \left [ \vec{a}\;\vec{c}\; \vec{d}\right ]+\left [ \vec{b}\;\vec{c}\; \vec{d} \right ]

- wherein

\vec{a}, \vec{b}, \vec{c}, \vec{d} are four vectors.

 

 

[ \vec{a}\; \; \vec{b}\; \; \vec{c}]\neq 0

We have  ,  [ \lambda (\vec{a}+\vec{b})\; \; \lambda ^2\vec{b}\; \; \lambda \vec{c}]

 

\lambda ^4 [ (\vec{a}+\vec{b})\; \;\vec{b}\; \; \vec{c}]

\lambda ^4 [ \vec{a}\; \;\vec{b}\; \; \vec{c}]

[ \vec{a}\; \; \; \vec{b}+\vec{c}\; \; \; \vec{b}]= [ \vec{a}\; \;\vec{b}\; \; \vec{c}]\\ \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; \; = - [ \vec{a}\; \;\vec{b}\; \; \vec{c}]

So , \lambda ^4 = -1   no real value of \lambda

 

 

 

 

 

 

 

 


Option 1)

no value of \lambda

Option 2)

exactly one value of \lambda

Option 3)

exactly two values of \lambda

Option 4)

exactly three values of \lambda

Posted by

Himanshu

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2024 session 2 final answer key soon at jeemain.nta.ac.in; result on April 25
anam-khan

JEE Main 2024 Session 2: Last day to challenge answer key today
anam-khan

BTech admission 2024 without JEE; top government engineering colleges, upcoming entrance exams

Latest Question