Q. If the lines $x + 3y - 9 = 0,\ 4x + by - 2 = 0$ and $2x - y - 4 = 0$ are concurrent, then $b$ equals
A) $- 5$
B) 5
C) 1
D) 0
Explanation
(a)
Given lines are concurrent, then
$\left| \begin{matrix}
1 & 3 & - 9 \\
4 & b & - 2 \\
2 & - 1 & - 4
\end{matrix} \right| = 0$
$\Rightarrow \ 1( - 4b - 2) - 3( - 16 + 4) - 9( - 4 - 2b) = 0$
$\Rightarrow \ 14b + 70 = 0\ \Rightarrow \ b = - 5$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.