Chat with tutor

Ask Questions, Get Answers

Questions  >>  JEEMAIN and NEET  >>  Mathematics  >>  Class11  >>  3-D Geometry

Equation of the line through the point $(2,-1,-1)$, which is parallel to the plane $4x+y+z+2=0$ ans is $\perp$ to the line $x=\large\frac{y}{-2}=$$z-5$ is ?


1 Answer

Given: Eqn. of the plane $4x+y+z+2=0$ ......(i)
Eqn. of the line is $\large\frac{x}{1}=\frac{y}{-2}=\frac{z-5}{1}$$=\lambda$.....(ii)
A line parallel to the plane (i) is $\perp$ to the normal, $ \overrightarrow n=(4,1,1)$ to (i)
A line $\perp$ to (ii) and $\overrightarrow n$ has $d.r. = \overrightarrow n\times (1,-2,1)$
(Since a vector $\perp$ to $\overrightarrow a\:\:and\:\:\overrightarrow b$ is $\overrightarrow a\times\overrightarrow b$)
$(4,1,1)\times (1,-2,1)=(3,-3,9)$
$\therefore$ $d.r.$ of the required line is $(-3,3,9)=(-1,1,3)$
$\therefore$ The eqn, of the required line through $(2,-1,-1)$ is
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.