We are given with the Cartesian equation of two lines and their direction ratios are in the form of some variable we need to find the value of this variable so that these lines are perpendicular to each other. We can use the dot product equation to solve this problem, which is,

a₁a₂+b₁b₂+c₁c₂ = 0

the equation of the lines are,

By using the direction ratios of these lines in the dot product equation, we get,

(–3)3k + 2k(1) + 2(–5) = 0

–9k + 2k – 10 = 0

k =