If the line 3x - 4y + 7 = 0 and 2x + ky + 5 = 0 are perpendicular to each other, then the value of k is

1. $\dfrac{3}{2}$

2. $-\dfrac{3}{2}$

3. $\dfrac{2}{3}$

4. $-\dfrac{2}{3}$

Given,

3x - 4y + 7 = 0 and
2x + ky + 5 = 0

⇒ 4y = 3x + 7 and ky = -2x - 5

⇒ y = $\dfrac{3}{4}x + \dfrac{7}{4}$ and y = $-\dfrac{2}{k}x - \dfrac{5}{k}$

Comparing both the equations with y = mx + c,

Slope of first line = m₁ = $\dfrac{3}{4}$

Slope of second line = m₂ = $-\dfrac{2}{k}$

Since, both the lines are perpendicular so,

$\Rightarrow m$1 \times m2 = -1 \\[1em] \Rightarrow \dfrac{3}{4} \times -\dfrac{2}{k} = -1 \\[1em] \Rightarrow k = \dfrac{3 \times -2}{4 \times -1}\\[1em] \Rightarrow k = \dfrac{6}{4} = \dfrac{3}{2}.

Hence, Option 1 is the correct option.