Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

The magnitude of the projection of the vector 2\hat{i}+3\hat{j}+\hat{k} on the vector perpendicular to the plane containing the vectors \hat{i}+\hat{j}+\hat{k} and \hat{i}+2\hat{j}+3\hat{k} is :

 

  • Option 1)

    \sqrt{\frac{3}{2}}

  • Option 2)

    \sqrt{6}

  • Option 3)

    \frac{\sqrt{3}}{2}

     

  • Option 4)

    3\sqrt{6}

 

Answers (1)

best_answer

Normal vector to plane containing vector \hat{i}+\hat{j}+\hat{k}

and \hat{i}+2\hat{j}+3\hat{k} is

\hat{n}=(\hat{i}+\hat{j}+\hat{k})\times(\hat{i}+2\hat{j}+3\hat{k})

\hat{n}=\hat{i}-2\hat{j}+\hat{k}

Projection of 2\hat{i}+3\hat{j}+\hat{k} on \hat{n}

=\left | \frac{(2\hat{i}+3\hat{j}+\hat{k})(\hat{i}-2\hat{j}+\hat{k})}{\sqrt{1+4+1}} \right |

=\frac{3}{\sqrt{6}}=\sqrt{\frac{3}{2}}


Option 1)

\sqrt{\frac{3}{2}}

Option 2)

\sqrt{6}

Option 3)

\frac{\sqrt{3}}{2}

 

Option 4)

3\sqrt{6}

Posted by

solutionqc

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 aspirant from north-east or UT? Apply for CSAB NEUT counselling 2025 today
anam-khan

JoSAA round 2 cut-off 2025 out; BTech closing ranks for top engineering courses at IITs
anam-khan

Goa Engineering Admission 2025: 1,415 eligible for BE seats; merit list on June 27

Latest Question