Lines mx + 3y = -7 and 5x - ny = 3 are perpendicular to each other. Find the relation connecting m and n.

Given lines,

⇒ mx + 3y = -7 and 5x - ny = 3

⇒ 3y = -mx - 7 and ny = 5x - 3

⇒ y = $-\dfrac{m}{3}x - \dfrac{7}{3}$ and $y = \dfrac{5}{n}x - \dfrac{3}{n}$

Comparing above equations with y = mx + c we get,

Slope of 1st line = $-\dfrac{m}{3}$

Slope of 2nd line = $\dfrac{5}{n}$

Since, product of slopes of perpendicular lines = -1.

$\therefore -\dfrac{m}{3} \times \dfrac{5}{n} = -1 \\[1em] \Rightarrow -\dfrac{5m}{3n} = -1 \\[1em] \Rightarrow 5m = 3n \\[1em] \Rightarrow 5m - 3n = 0.$

Hence, relation connecting m and n is 5m - 3n = 0.