If line $2 x + 3 y + 4 = 0$ is perpendicular to $3 x - a y + 5 = 0$ then $a = ?$

\frac{3}{2}

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\frac{2}{3}

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\frac{5}{3}

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Solution

The correct option is C 2
Line $2 x + 3 y + 4 = 0$ is perpendicular to $3 x - a y + 5 = 0$
Consider the line $2 x + 3 y + 4 = 0$
$y = \frac{- 2}{3} x - \frac{4}{3}$
The slope of the above line is $m_{1} = \frac{- 2}{3}$
The other line,
$3 x - a y + 5 = 0 y = \frac{3}{a} x + \frac{5}{a}$
The slope of the line is $m_{2} = \frac{3}{a}$
Using the condition of perpendicularity we can write
$m_{1} . m_{2} = - 1 \Rightarrow \frac{- 2}{3} \times \frac{3}{a} = - 1 \Rightarrow a = 2$

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