Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Need clarity, kindly explain! - Vector Algebra - JEE Main-2

if \left | \vec{c} \right |^{2}=60\; and\; \vec{c}\times (\hat{i}+2\hat{j}+5\hat{k})=\vec{0}, then a value of  \left \vec{c} \right \cdot (-7\hat{i}+2\hat{j}+3\hat{k})\; is\, \; :   

  • Option 1)

    4\sqrt{2}

  • Option 2)

    12

  • Option 3)

    24

  • Option 4)

    12\sqrt{2}

 

Answers (1)

best_answer

As we learnt in 

Collinear Vectors -

Two vectors are said to be collinear if and only if there exists a scalar m such as that \vec{a}=m\vec{b}

- wherein

m is a Scalar.

 

 \vec{c}\times (\vec{i}+\vec{2j}+\vec{5k})=\vec{0}

So\:\vec{c}\:and (\vec{i}+\vec{2j}+\vec{5k})\:are\:collinear

\vec{c}=P(\vec{i}+\vec{2j}+\vec{5k})

\left |\vec{c} \right |^{2}=P^{2}\times (1^{2}+2^{2}+5^{2})=60\Rightarrow P^{2}=2

value= \vec{c}.(-7\vec{i}+2\vec{j}+3\vec{k})

=\sqrt{2}(\vec{i}+2\vec{j}+5\vec{k}).(-7\vec{i}+2\vec{j}+3\vec{k})

=\sqrt{2}(-7+4+15)=12\sqrt{2}

Correct option is 4.


Option 1)

4\sqrt{2}

This option is incorrect 

Option 2)

12

This option is correct 

Option 3)

24

This option is incorrect 

Option 4)

12\sqrt{2}

This option is  incorrect 

Posted by

Aadil

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

BTech Admission 2025 Live: JEE Mains, SRMJEEE, MET registrations underway; MHT CET syllabus updates
anam-khan

Centre issues coaching guidelines, prohibits centres from using false claims like '100% selection'
anam-khan

BTech Admissions 2025 Live: JEE Mains, SRMJEE, VITEEE dates out; AEEE, MET registrations underway

Latest Question