Straight Line Question 52

Question: The three lines $ lx+my+n=0 $ , $ mx+ny+l=0 $ , $ nx+ly+m=0 $ are concurrent if [Pb. CET 2002]

Options:

A) $ l=m+n $

B) $ m=l+n $

C) $ n=l+m $

D) $ l+m+n=0 $

Show Answer

Answer:

Correct Answer: D

Solution:

  • $ | \begin{matrix} l & m & n \\ m & n & l \\ n & l & m \\ \end{matrix} |=0\Rightarrow \begin{vmatrix} l+m+n & m & n \\ l+m+n & n & l \\ l+m+n & l & m \\ \end{vmatrix} =0 $
    Þ $ (l+m+n)| \begin{matrix} 1 & m & n \\ 1 & n & l \\ 1 & l & m \\ \end{matrix} |=0\Rightarrow (l+m+n)=0 $ .