Question

Find the value of $\lambda$, if the lines $3x-4y-13=0,8x-11y-33=0$ and $2x-3y+\lambda =0$ are concurrent

• A. $\lambda =7$
• B. $\lambda =-7$
• C. $\lambda =-3$
• D. $\lambda =3$

Answer 1

The correct option is B $\lambda =-7$

Lines are concurrent when

$\left|\begin{array}{ccc}{A}_1& B_1& C_1\\ A_2& B_2& C_2\\ A_3& B_3& C_3\end{array}\right|=0$

So, $\left|\begin{array}{ccc}3& -4& -13\\ 8& -11& -33\\ 2& -3& \lambda \end{array}\right|=0\Rightarrow 3(-11\lambda -99)+4(8\lambda +66)-13(-24+22)=0\Rightarrow -33\lambda -297+32\lambda +264+26=0\Rightarrow \lambda =-7$