We know that equation of plane passing through the line of intersection of planes

(a₁x + b₁y + c₁z + d₁) + k(a₂x + b₂y + c₂z + d₂) = 0

So equation of plane passing through the line of intersection of planes

x – 3y + 2z – 5 = 0 and 2x – y + 3z – 1 = 0 is given by

(x – 3y + 2z – 5) + k(2x – y + 3z – 1) = 0

x(1 – 2k) + y( – 3 – k) + z(2 + 3k) – 5 – k = 0 …… (1)

Given that plane (1) is perpendicular if

a₁a₂ + b₁b₂ + c₁c₂ = 0 ……(2)

We know that two planes are perpendicular to plane,

5x + 3y + 6z + 8 = 0 ……(3)

Using (1) and (3) in equation (2),

5(1 + 2k) + 3(2 + k) + 6(3 – k) = 0

5 + 10k + 6 + 3k + 18 – 6k = 0

29 + 7k = 0

7k = – 29

Put the value of k in equation (1),

= 0

51 x + 15 y – 50 z + 173 = 0