Email
Chat with tutor
logo

Ask Questions, Get Answers

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

If $\mid\overrightarrow{a}\mid=4$ and $-3\leq\:\lambda\leq 2$,then the range of $\mid\lambda\overrightarrow{a}\mid$ is

\[(A)\;[0,8]\quad(B)\;[-12,8]\quad(C)\;[0,12]\quad(D)\;[8,12]\]

1 Answer

Comment
A)
Toolbox:
  • $|\lambda\:\overrightarrow a|=|\lambda||\overrightarrow a|$
Given $|\overrightarrow a|=4 \: and\:-3\leq\lambda\leq\:2$
Since it is given $-3 \leq \lambda \leq 2$
This implies $0\leq|\lambda|\leq\:3$
Multiply this in equation by $ |\overrightarrow a|$ we get,
$=>0\leq|\lambda|\:|\overrightarrow a|\leq\:3|\overrightarrow a|$
But $|\lambda|\:|\overrightarrow a|=|\lambda\overrightarrow a|$ and $|\overrightarrow a|=4$
$=>0\leq\:|\lambda\overrightarrow a|\leq\:3\times4$
$=>0\leq\:|\lambda\overrightarrow a|\leq 12$
Hence the range of $\lambda \: is\: [0,12]$
Hence $C$ is the correct option
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.
...