In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.

4x + 8y + z – 8 = 0 and y + z – 4 = 0

The eq. of the given planes are

4x + 8y + z – 8 = 0 and y + z – 4 = 0

Two planes are ⊥ if the direction ratio of the normal to the plane is

a₁a₂ + b₁b₂ + c₁c₂ = 0

0 + 8 + 1

9 ≠ 0

∴ Both the planes are not ⊥ to each other.

Two planes are || to each other if the direction ratio of the normal to the plane is

∴ Both the planes are not || to each other.

The angle between them is given by

= 45⁰