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


a1a2 + b1b2 + c1c2 = 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