Email
Chat with tutor
logo

Ask Questions, Get Answers

X
 
Answer
Comment
Share
Q)

If $\overrightarrow{a}\times \overrightarrow{b}= \overrightarrow{C}\times \overrightarrow{d}$ and $\overrightarrow{a}\times \overrightarrow{c}=\overrightarrow{b}\times\overrightarrow{d},$ show that $\overrightarrow{a}- \overrightarrow{d}$ and $\overrightarrow{b}-\overrightarrow{c}$ are parallel.

1 Answer

Comment
A)
Toolbox:
  • $ \overrightarrow a \times \overrightarrow b = -(\overrightarrow b \times \overrightarrow a)\: or \: \overrightarrow b \times \overrightarrow a = -(\overrightarrow a \times \overrightarrow b)$ and $ \overrightarrow a \times ( \overrightarrow b + \overrightarrow c) = \overrightarrow a \times \overrightarrow b + \overrightarrow a \times \overrightarrow c$
  • If $ \overrightarrow a \: and \: \overrightarrow c $ are parallel vectors then $\overrightarrow a \times \overrightarrow c = \overrightarrow 0$
Consider $ (\overrightarrow a-\overrightarrow d) \times (\overrightarrow b-\overrightarrow c) $
$ = \overrightarrow a \times ( \overrightarrow b - \overrightarrow c)-\overrightarrow d \times (\overrightarrow b-\overrightarrow c)$
$ = \overrightarrow a \times \overrightarrow b - \overrightarrow a \times \overrightarrow c - \overrightarrow d \times \overrightarrow b + \overrightarrow d \times \overrightarrow c$
$ = \overrightarrow a \times \overrightarrow b - \overrightarrow a \times \overrightarrow c + \overrightarrow b \times \overrightarrow d - \overrightarrow c \times \overrightarrow d$
$ = \overrightarrow a \times \overrightarrow b-\overrightarrow c \times \overrightarrow d + \overrightarrow b \times \overrightarrow d - \overrightarrow a \times \overrightarrow c$
$ \overrightarrow 0$ [ Since $ \overrightarrow a \times \overrightarrow b = \overrightarrow c \times \overrightarrow d \: and \: \overrightarrow b \times \overrightarrow d = \overrightarrow a \times \overrightarrow c]$
Now $(\overrightarrow a-\overrightarrow d) \times ( \overrightarrow b-\overrightarrow c)=\overrightarrow 0 \Rightarrow (\overrightarrow a-\overrightarrow d) \parallel ( \overrightarrow b-\overrightarrow c)$
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.
...