Find the value of p if the lines, whose equations are 2x – y + 5 = 0 and px + 3y = 4 are perpendicular to each other.

Given lines,

⇒ 2x - y + 5 = 0 and px + 3y = 4

⇒ y = 2x + 5 and 3y = -px + 4

⇒ y = 2x + 5 and y = $-\dfrac{p}{3}x + \dfrac{4}{3}$.

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

Slope of 1st line = 2

Slope of 2nd line = $-\dfrac{p}{3}$

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

$\therefore 2 \times -\dfrac{p}{3} = -1 \\[1em] \Rightarrow -p = \dfrac{-1 \times 3}{2} \\[1em] \Rightarrow -p = -\dfrac{3}{2} \\[1em] \Rightarrow p = \dfrac{3}{2}.$

Hence, p = $\dfrac{3}{2}$.