Given planes, x – 2y + 4z = 10 and 18x + 17y + 4z = 49

We know that planes a₁x + b₁y + c₁z + d₁ = 0 and a₂x + b₂y + c₂z + d₂ = 0 are at right angles if,

a₁a₂ + b₁b₂ + c₁c₂ = 0 …… (a)

We have, a₁ = 1, b₁ = – 2, c₁ = 4 and a₂ = 18, b₂ = 17, c₂ = 4

Using (a) we have,

a₁a₂ + b₁b₂ + c₁c₂ = (1)(18) + (– 2)(17) + (4)(4)

= 18 – 34 + 16 = 0

Hence, the planes are at right angle to each other.