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 $\overrightarrow a,\:\overrightarrow b,\:\overrightarrow c$ are any three unit vectors such that $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c=0$ and the angle between $\overrightarrow b\:\:and\:\:\overrightarrow c $ is $\large\frac{\pi}{6}$, then $\overrightarrow b\times\overrightarrow c=?$

Can you answer this question?

1 Answer

0 votes
Given: $\overrightarrow a.\overrightarrow b=\overrightarrow a.\overrightarrow c=0$
$\Rightarrow\:\overrightarrow a $ is $\perp$ to both $\overrightarrow b\:\:and\:\:\overrightarrow c$
$\Rightarrow\:\overrightarrow a=\lambda (\overrightarrow b\times\overrightarrow c)$
$\Rightarrow\:|\overrightarrow a|=|\lambda|.|\overrightarrow b\times\overrightarrow c|$
$\Rightarrow\:|\overrightarrow a|=|\lambda|.|\overrightarrow b||\overrightarrow c|. sin\large\frac{\pi}{6}$
(Since $\overrightarrow a,\overrightarrow b,\overrightarrow c$ are unit vectors and the angle between $\overrightarrow b\:\overrightarrow c$ is $\large\frac{\pi}{6})$
or $\lambda=\pm 2$
$\Rightarrow\:\overrightarrow a=\pm (\overrightarrow b\times\overrightarrow c)$
$\Rightarrow\:\overrightarrow b\times\overrightarrow c=\pm\large\frac{1}{2}$$\overrightarrow a$
answered Dec 5, 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