Chat with tutor

Ask Questions, Get Answers

Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class12  >>  Vector Algebra

If $\overrightarrow a=2\hat i+\hat j-2\hat k\:\:and\:\:\overrightarrow b=\hat i+\hat j.$ and $\overrightarrow c$ is a vector such that $\overrightarrow a.\overrightarrow c=|\overrightarrow c|,\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2 $ and angle between $\overrightarrow a\times\overrightarrow b\:\:and\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$, then $|(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c|=?$

1 Answer

Given: $\overrightarrow a.\overrightarrow c=|\overrightarrow c|\:\:and\:\:|\overrightarrow c-\overrightarrow a|=2\sqrt 2$
$\Rightarrow\:|\overrightarrow c-\overrightarrow a|^2=8$
$\Rightarrow\:|\overrightarrow c|^2+|\overrightarrow a|^2-2\overrightarrow c.\overrightarrow a=8$
$\Rightarrow\:|\overrightarrow c|^2+9-2|\overrightarrow c|=8$
(Since it is given that $\overrightarrow a=2\hat i+\hat j-2\hat k,\:\:\:|\overrightarrow a|=3$)
$\therefore |\overrightarrow c|=1$
$(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c=|\overrightarrow a\times\overrightarrow b||\overrightarrow c|sin\large\frac{\pi}{6}$
(Since it is given that the angle between $\overrightarrow a\times\overrightarrow b\:\:\:and\:\:\:\overrightarrow c$ is $\large\frac{\pi}{6}$.)
$\Rightarrow\:(\overrightarrow a\times\overrightarrow b)\times\overrightarrow c=\large\frac{1}{2}$$|\overrightarrow a\times\overrightarrow b|$
$=\large\frac{1}{2}$$|2\hat i-2\hat j+\hat k|=\large\frac{3}{2}$
Since $\overrightarrow a\times\overrightarrow c=2\hat i-2\hat j+\hat k$
Help Clay6 to be free
Clay6 needs your help to survive. We have roughly 7 lakh students visiting us monthly. We want to keep our services free and improve with prompt help and advanced solutions by adding more teachers and infrastructure.

A small donation from you will help us reach that goal faster. Talk to your parents, teachers and school and spread the word about clay6. You can pay online or send a cheque.

Thanks for your support.
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Clay6 tutors use Telegram* chat app to help students with their questions and doubts.
Do you have the Telegram chat app installed?
Already installed Install now
*Telegram is a chat app like WhatsApp / Facebook Messenger / Skype.