The equation of a plane passing through (x₁,y₁,z₁) and perpendicular to a line with direction ratios A, B, C is

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

The plane passes through (a,b,c)

So, x₁ = a, y₁ = b, z₁ = c

Since both planes are parallel to each other, their normal will be parallel

∴ Direction ratios of normal

= Direction ratios of normal of

Direction ratios of normal = (1,1,1)

∴ A = 1, B =1, C = 1

Thus,

Equation of plane in cartesian form is

A(x - x₁) + B(y - y₁) + C(z - z₁) = 0

⇒ 1(x - a) + 1(y - b) + 1(z - c) = 0

⇒ x + y + z - (a + b + c) = 0

Thus, x + y + z = a + b + c is the required equation of plane.