The lines find the value of $k$ if the lines $3 x + 5 y + 9 = 0 7 x + k y + 3 = 0$ are perpendicular to each other.

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Solution

$3 x + 5 y + 9 = 0 m_{1} = \frac{- 3}{5} 7 x + k y + 3 = 0 m_{2} = \frac{- 7}{k} m_{1} m_{2} = - 1 \frac{- 3}{5} \times \frac{- 7}{k} = - 1 k = \frac{- 21}{5}$

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