Statement-I The lines $2 x + 3 y + 5 = 0$ and $3 x - 2 y + 6 = 0$ are perpendicular lines.
$Statement - II If m_{1}, m_{2} are the slopes of two mutually non vertical perpendicular lines, then m_{1} \cdot m_{2} = - 1$

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Statement I is False, Statement II is True

Statement I is True, Statement II is True

Statement I is True, Statement II is False

Statement I is False, Statement II is False

answer is A.

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Detailed Solution

L_{1} = 2 x + 3 y + 5 = 0

$L_{2} = 3 x - 2 y + 6 = 0$

Slope $(L_{1}) = m_{1} = \frac{- a}{b} = \frac{- 2}{3}$

Slope $L_{2} = m_{2} = \frac{- a}{b} = \frac{- 3}{- 2} = \frac{3}{2}$

$∴$ $m_{1} . m_{2} = \frac{- 2}{3} \times \frac{3}{2} = - 1$

$∴$ $L_{1} & L_{2}$ are perpendicular lines

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