The line of intersection of two planes r · n₁ = p₁ and r · n₂ = p₂ lies in both planes. It is therefore perpendicular to both n₁ and n₂. Give an expression for this direction, and so show that the equation of the line of intersection may be written as r = r₀ + t(n₁ × n₂), where r₀ is any vector satisfying r₀ · n₁ = p₁ and r₀ · n₂ = p₂. Hence find the line of intersection of the planes r · (1, 1, 1) = 5 and r · (4, 1, 2) = 15.