Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa

Let three vector \vec{a},\vec{b} and \;\vec{c}\; be such that \;\vec{c}\; is coplanar with \;\vec{a}\; and \vec{b}, \vec{a}\cdot\vec{b}=7 and \vec{b} is perpendicular to \vec{c}, where \vec{a}=-\hat{i}+\hat{j}+\hat{k} and \vec{b}=2\hat{i}+\hat{k}. Then the value of 2\left | \vec{a}+\vec{b}+\vec{c}\; \right |^2 is ___________
Option: 1 75
Option: 2 50
Option: 3 25
Option: 4 100

Answers (1)

best_answer

 

\\\overrightarrow{\mathrm{c}}=\lambda(\overrightarrow{\mathrm{b}} \times(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})) \\ \\ {\;\;\;}=\lambda((\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{b}}) \overrightarrow{\mathrm{b}}-(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{a}}) \overrightarrow{\mathrm{b}}) \\ \\ {\;\;\;}=\lambda(5(-\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}})+2 \hat{\mathrm{i}}+\hat{\mathrm{k}}) \\ \\ {\;\;\;}=\lambda(-3 \hat{\mathrm{i}}+5 \hat{\mathrm{j}}+6 \hat{\mathrm{k}})

\overrightarrow{\mathrm{c}} \cdot \overrightarrow{\mathrm{a}}=7 \Rightarrow 3 \lambda+5 \lambda+6 \lambda=7

\Rightarrow\lambda=\frac{1}{2}

\\\therefore 2\left|\left(\frac{-3}{2}-1+2\right) \hat{i}+\left(\frac{5}{2}+1\right) \hat{j}+(3+1+1) \hat{k}\right|^{2} \\ \\=2\left(\frac{1}{4}+\frac{49}{4}+25\right)=25+50=75

Posted by

Suraj Bhandari

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 Result 2024 Live: JEE Mains session 2 results at jeemain.nta.ac.in soon; rank predictor
anam-khan

JEE Main 2024 session 2 final answer key out at jeemain.nta.ac.in; steps to check probable scores
anam-khan

JEE Main Result 2024 Live: Download session 2 final answer key at jeemain.nta.ac.in; rank predictor, cutoff

Latest Question