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Question
If the lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent, then the value of q will be
Options
1
2
3
5
Solution
3
The lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent.
\[\therefore \begin{vmatrix}1 & 0 & q \\ 0 & 1 & - 2 \\ 3 & 2 & 5\end{vmatrix} = 0\]
\[ \Rightarrow 1\left( 5 + 4 \right) - 0 + q\left( 0 - 3 \right) = 0\]
\[ \Rightarrow 3q = 9\]
\[ \Rightarrow q = 3\]
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