We are given with the Cartesian equations of two lines and their direction ratios are in the form of variables, we need to find the value of this variable and give the complete equation, it is also given that the lines are perpendicular to each other.

The equations of the lines are,

These are not in their standard form, so after converting them, we get

Now as we know the direction ratios of both the lines, so by using the dot product equation, we get,

a₁a₂+b₁b₂+c₁c₂ = 0

(5λ+2)1+(–5)2λ+1(3) = 0

5λ+2–10λ+3 = 0

–5λ+5 = 0

λ = 1