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

2x – 2y + 4z + 5 = 0 and 3x – 3y + 6z – 1 = 0

The eq. of the given planes are

2x – y + 3z – 1 = 0 and 2x – y + 3z + 3 = 0

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

a_{1}a_{2} + b_{1}b_{2} + c_{1}c_{2} = 0

2 × 2 + (-1) × (-1) + 3 × 3

14 ≠ 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

Thus, the given planes are || to each other.

13