If lines x + 2ay + a = 0 , x + 3by + b = 0 and x + 4cy + c = 0 are concurrent, then a , b and

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3 and 4 .Determinants and Matrices

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If the lines $x + 2ay + a = 0$, $x + 3by + b = 0$ and $x + 4cy + c = 0$ are concurrent, then $a$, $b$ and $c$ are in

A

$A.P.$

B

$G.P.$

C

$H.P.$

D

None of these

Solution

Given lines will be concurrent if

$\left|\begin{array}{lll}{1} & {2 a} & {a} \\ {1} & {3 b} & {b} \\ {1} & {4 c} & {c}\end{array}\right|=0 \Rightarrow-b c+2 a c-a b=0$

$\Rightarrow \mathrm{b}=\frac{2 \mathrm{ac}}{\mathrm{a}+\mathrm{c}} \Rightarrow \mathrm{a}, \mathrm{b}, \mathrm{c}$ are in $\mathrm{H.} \mathrm{P.}$

Standard 12

Mathematics

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