Question

If the lines $2x-ay+1=0$,$3x-by+1=0$,$4x-cy+1=0$ are concurrent then $a,b,c$ are in ?
.

• A. G.P.
• B. A.P.
• C. H.P.
• D. A.G.P.

Answer 1

The correct option is B A.P.

$2x-ay+1=0,3x-by+1=0,4x-cy+1=0$

Given lines are concurrent

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

$\Rightarrow 2b-a-c=0$

$\Rightarrow 2b=a+c$

Hence, a,b,c are in A.P.