The three lines lx + my + n = 0,mx + ny + l = | vedclass

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(D) For the three lines to be concurrent,the determinant of the coefficients must be zero: $\begin{vmatrix} l & m & n \ m & n & l \ n & l & m \end{v

Vedclass · Accepted Answer

$l + m + n = 0$

Vedclass · Answer

(D) For the three lines to be concurrent,the determinant of the coefficients must be zero: $\begin{vmatrix} l & m & n \ m & n & l \ n & l & m \end{vmatrix} = 0$ Applying the column operation $C_1 	o C_1 + C_2 + C_3$: $\begin{vmatrix} l + m + n & m & n \ l + m + n & n & l \ l + m + n & l & m \end{vmatrix} = 0$ Factoring out $(l + m + n)$: $(l + m + n) \begin{vmatrix} 1 & m & n \ 1 & n & l \ 1 & l & m \end{vmatrix} = 0$ Thus,the condition for concurrency is $l + m + n = 0$.

The three lines $lx + my + n = 0$,$mx + ny + l = 0$,and $nx + ly + m = 0$ are concurrent if:

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