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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, c are in

Option: 1

A.P 


Option: 2

G.P 


Option: 3

H.P 


Option: 4

None of these 


Answers (1)

best_answer

Condition of concurrency

\begin{vmatrix} a_{1} & b_{1} & c_{1}\\ a_{2}& b_{2} &c_{2} \\ a_{3} & b_{3} &c_{3} \end{vmatrix}=0
Applying it to given question

\begin{vmatrix} 1 & 2a & a\\ 1 & 3b &b \\ 1& 4c & c \end{vmatrix}=0 

3bc -4bc - 2a (c - b) + a (4c - 3b) = 0

- bc + 2ac - ab = 0   \Rightarrow     \frac{2}{b} = \frac{1}{a} + \frac{1}{c}

So a, b, c are in H.P.

Posted by

HARSH KANKARIA

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