If the lines 3x + y - 2 = 0,px + 2y - 3 = 0,a | vedclass

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(B) Three lines are concurrent if the determinant of their coefficients is zero. The given lines are $3x + y - 2 = 0$,$px + 2y - 3 = 0$,and $2x - y -

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Three lines are concurrent if the determinant of their coefficients is zero. The given lines are $3x + y - 2 = 0$,$px + 2y - 3 = 0$,and $2x - y - 3 = 0$. The condition for concurrency is: $\begin{vmatrix} 3 & 1 & -2 \ p & 2 & -3 \ 2 & -1 & -3 \end{vmatrix} = 0$ Expanding the determinant along the first row: $3(2(-3) - (-1)(-3)) - 1(p(-3) - 2(-3)) - 2(p(-1) - 2(2)) = 0$ $3(-6 - 3) - 1(-3p + 6) - 2(-p - 4) = 0$ $3(-9) + 3p - 6 + 2p + 8 = 0$ $-27 + 3p - 6 + 2p + 8 = 0$ $5p - 25 = 0$ $5p = 25$ $p = 5$ Thus,the correct option is $B$.

If the lines $3x + y - 2 = 0$,$px + 2y - 3 = 0$,and $2x - y - 3 = 0$ are concurrent,then $p =$

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