Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • If the volume of a parallelopiped, whose coterminous edges are given by the vectors 

If the volume of a parallelopiped, whose coterminous edges are given by the vectors  \vec{a}=\hat{i}+\hat{j}+n\hat{k},\; \vec{b}=2\hat{i}+4\hat{j}-n\hat{k} and \vec{c}=\hat{i}+n\hat{j}+3\hat{k}\; (n\geqslant 0), is 158\; cu.units, then :
Option: 1 \vec{a}\cdot \vec{c}=17  
Option: 2 \vec{b}\cdot \vec{c}=10
Option: 3 n=7
Option: 4 n=9

Answers (1)

best_answer

\\\mathrm{v}=[\overrightarrow{\mathrm{ab}} \overrightarrow{\mathrm{c}}] \\ 158=\left|\begin{array}{ccc} 1 & 1 & \mathrm{n} \\ 2 & 4 & -\mathrm{n} \\ 1 & \mathrm{n} & 3 \end{array}\right|, \mathrm{n} \geq 0 \\ 158=1\left(12+\mathrm{n}^{2}\right)-(6+\mathrm{n})+\mathrm{n}(2 \mathrm{n}-4) \\ 158=\mathrm{n}^{2}+12-6-\mathrm{n}+2 \mathrm{n}^{2}-4 \mathrm{n} \\ 3 \mathrm{n}^{2}-5 \mathrm{n}-152=0

\mathrm{n}=8,-\frac{38}{6} \text { (rejected) } \\ {\mathrm{\vec a}\cdot \vec{\mathrm{c}}}=1+\mathrm{n}+3 \mathrm{n}=1+4 \mathrm{n}=33 \\ \vec{\mathrm{b}} \cdot \vec{\mathrm{c}}=2+4 \mathrm{n}-3 \mathrm{n}=2+\mathrm{n}=10

Posted by

himanshu.meshram

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 April results at jeemain.nta.ac.in likely today; cutoff, rank predictor, update
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