Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Questions  >>  CBSE XII  >>  Math  >>  Vector Algebra
Answer
Comment
Share
Q)

What is the area of the parallelogram having diagonals $ 3\bar{i}+\bar{j}-2\bar{k}\;and\;\bar{i}-3\bar{j}+4\bar{k}$?

$\begin{array}{1 1} 5 \sqrt 3 \\ 10 \sqrt 3 \\ 8 \\ 4 \end{array} $

1 Answer

Comment
A)
Toolbox:
  • Area of parallelogram =$\large\frac{1}{2}|$$\overrightarrow a\times\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are diagonals of the prarallelogram.
  • $\overrightarrow a\times\overrightarrow b=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{array}\right|$
Given that $\overrightarrow a=3\hat i+\hat j-2\hat k$ and
$\overrightarrow b=\hat i-3\hat j+4\hat k$ are diagonals of the parallelogram.
We know that$\overrightarrow a\times\overrightarrow b=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\a_1&a_2&a_3\\b_1&b_2&b_3\end{array}\right|$
$=\left|\begin{array}{ccc}\hat i&\hat j&\hat k\\3&1&-2\\1&-3&4\end{array}\right|$ $=\:\hat i(4-6)-\hat j(12-(-2))+\hat k(-9-1)$
$=-2\hat i-14\hat j-10\hat k$
$|\overrightarrow a\times\overrightarrow b|=\sqrt{(-2)^2+(-14)^2+(-10)^2}$
$=\sqrt{4+196+100}=\sqrt{300}=10\sqrt3$
We know that area of the parallelogram =$\large\frac{1}{2}|$$\overrightarrow a\times\overrightarrow b|$ where $\overrightarrow a\:\:and\:\:\overrightarrow b$ are diagonals of the prarallelogram.
Area of the parallelogram $=\large\frac{1}{2}$$10\sqrt3=5\sqrt3 \approx 8.66$
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.
Continue
Please choose your payment mode to continue
Home Ask Homework Questions
Your payment for is successful.
Continue
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.
...