If the lines ax + 2y + 1 = 0,bx + 3y + 1 = 0, | vedclass

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(A) The given lines are $ax + 2y + 1 = 0$,$bx + 3y + 1 = 0$,and $cx + 4y + 1 = 0$.Since these lines are concurrent,the determinant of their coefficien

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$A.P.$

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(A) The given lines are $ax + 2y + 1 = 0$,$bx + 3y + 1 = 0$,and $cx + 4y + 1 = 0$.Since these lines are concurrent,the determinant of their coefficients must be zero:$\begin{vmatrix} a & 2 & 1 \ b & 3 & 1 \ c & 4 & 1 \end{vmatrix} = 0$Expanding the determinant along the first row:$a(3 - 4) - 2(b - c) + 1(4b - 3c) = 0$$-a - 2b + 2c + 4b - 3c = 0$$-a + 2b - c = 0$$2b = a + c$This condition implies that $a, b, c$ are in $A.P.$

If the lines $ax + 2y + 1 = 0$,$bx + 3y + 1 = 0$,and $cx + 4y + 1 = 0$ are concurrent,then $a, b, c$ are in:

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