Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Class12  >>  Vector Algebra
0 votes

If $\overrightarrow a=\hat i+\hat j+\hat k\:\:\overrightarrow b=4\hat i+3\hat j+4\hat k\:\:and\:\:\overrightarrow c=\hat i+\alpha\hat j+\beta\hat k$ are linear dependent vectors and $|\overrightarrow c|=\sqrt 3$ then $ (\alpha,\beta)=?$

Can you answer this question?

1 Answer

0 votes
  • If $\overrightarrow a, \:\overrightarrow b\:\;and\:\:\overrightarrow c$ are linearly dependent, then $[\overrightarrow a\:\overrightarrow b\:\overrightarrow c]=0$
Given: $\overrightarrow a, \:\overrightarrow b\:\;and\:\:\overrightarrow c$ are linearly dependent,
$\Rightarrow\:\left |\begin {array}{ccc}1 & 1 & 1\\ 4 & 3 & 4\\1 & \alpha & \beta\end {array}\right|=0$
$\Rightarrow\:1-\beta=0$ or $\beta=1$
Also given that $|\overrightarrow c|=\sqrt 3$
$\Rightarrow\:\alpha=\pm 1$
$\therefore\:(\alpha,\beta)=(\pm 1,1)$
answered Nov 12, 2013 by rvidyagovindarajan_1

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, NEET Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App