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

Answer 1

3

The lines x + q = 0, y − 2 = 0 and 3x + 2y + 5 = 0 are concurrent.

\[\therefore \begin{vmatrix}1 & 0 & q \\ 0 & 1 & - 2 \\ 3 & 2 & 5\end{vmatrix} = 0\]

\[ \Rightarrow 1\left( 5 + 4 \right) - 0 + q\left( 0 - 3 \right) = 0\]

\[ \Rightarrow 3q = 9\]

\[ \Rightarrow q = 3\]