Q. The value of $k$ such that the lines $2x - 3y + k = 0,\ 3x - 4y - 13 = 0$ and $8x - 11y - 33 = 0$ are concurrent, is
A) 20
B) $- 7$
C) 7
D) $- 20$
Explanation
(b)
Given lines are concurrent
$\therefore\left| \begin{matrix}
2 & - 3 & k \\
3 & - 4 & - 13 \\
8 & - 11 & - 33
\end{matrix} \right| = 0$
$\Rightarrow \ 2(132 - 143) + 3( - 99 + 104) + k( - 33 + 32) = 0$
$\Rightarrow \ \ - 22 + 15 - k = 0\ \Rightarrow k = - 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.