Email
Chat with tutor
logo

Ask Questions, Get Answers

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

If $\overrightarrow{r}.\overrightarrow{a}=0,\overrightarrow{r}.\overrightarrow{b}=0$ and $\overrightarrow{r}.\overrightarrow{c}=0$ for some non-zero vector $\overrightarrow{r}$,then the value of $\overrightarrow{a}.(\overrightarrow{b}\times\overrightarrow{c})$ is___________.

$\begin{array}{1 1}0 \\ 1\\|\overrightarrow a| \\ |\overrightarrow b| \end{array} $

1 Answer

Comment
A)
Toolbox:
  • If $\overrightarrow a.\overrightarrow b =0$ then $\overrightarrow a\;\perp\;\overrightarrow b$
  • Such vectors are called orthogonal vectors.
$\overrightarrow r$ is a non zero vector, but it is given $\overrightarrow r.\overrightarrow a=0 \: and \: \overrightarrow r.\overrightarrow b=0\;and\;\overrightarrow r.\overrightarrow c=0$
This implies $\overrightarrow a.\overrightarrow b$ and $\overrightarrow c$ should be zero
Hence $ \overrightarrow a.(\overrightarrow b \times \overrightarrow c)=0$
Therefore If $\overrightarrow{r}.\overrightarrow{a}=0,\overrightarrow{r}.\overrightarrow{b}=0$ and $\overrightarrow{r}.\overrightarrow{c}=0$ for some non-zero vector $\overrightarrow{r}$,then the value of $\overrightarrow{a}.(\overrightarrow{b}\times\overrightarrow{c})$ is zero
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.
...