Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  • Let the plane containing the line of intersection of the planes <img alt="P 1: x+(\lambda+4) y+z=1 \text { and } P 2: 2 x+y+z=2" src="https://entrancecorner.oncodecogs.com/gif.latex?P%201%3A%2

Let the plane containing the line of intersection of the planes P 1: x+(\lambda+4) y+z=1 \text { and } P 2: 2 x+y+z=2pass through the points (0,1,0) and (1,0,1). Then the distance of the point (2 \lambda, \lambda,-\lambda) from the plane P2 is 

Option: 1

4 \sqrt{6}


Option: 2

3 \sqrt{6}


Option: 3

5 \sqrt{6}


Option: 4

2 \sqrt{6}


Answers (1)

best_answer

\begin{aligned} & {[x+(\lambda+4) \mathrm{y}+\mathrm{z}-1]+\mu[2 \mathrm{x}+\mathrm{y}+\mathrm{z}-2]=0} \\ & (0,1,0) \\ & \text { (i) }(\lambda+4-1)+\mu[-1]=0 \\ & \quad \lambda-\mu=-3 \\ & (1,0,1) \text { (ii) } 1+\mu[1]=0 \Rightarrow \mu=-1, \lambda=-4 \\ & \therefore \text { point }(-8,-4,4) ; 2 x+y+z-2=0 \\ & \qquad \mathrm{~d}=\left|\frac{-16-4+4-2}{\sqrt{6}}\right|=\frac{18}{\sqrt{6}}=3 \sqrt{6} \end{aligned}

Posted by

Gautam harsolia

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE

Similar Questions

Trending Articles/News

anam-khan

JEE Main 2025 Session 2 City Slip (OUT) Live: NTA exam city intimation slip link available; admit card date
anam-khan

AESL expands Aakash Digital 2.0 to offer AI-powered coaching for NEET, JEE, Olympiads
anam-khan

Bihar Board extends BSEB Super 50 free coaching application last date to March 26

Latest Question