Question

If the lines $2x+3y-13=0$, $x-4y+10=0$, $ax+5y-21=0$ are concurrent then the value of a is:

• A. $1$
• B. $2$
• C. $3$
• D. $-2$

Answer 1

Answer: (C)

$3$

As they are concurrent so determiant of coefficient matrix will be zero
$\left|\begin{array}{ccc}2& 3& -13\\ 1& -4& 10\\ a& 5& -21\end{array}\right|=2[84-50]-3[-21-10a]-13[5+4a]$
$\Rightarrow 68+63+30a-65-52a=0$
$\Rightarrow 66-22a=0$
$\Rightarrow a=3.$