Question
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
Solution
The given planes are
2x – 2 y + 4 z + 5 = 0 ...(1)
and 3 x – 3 y + 6 z – 1 = 0 ...(2)
Direction ratios of normal to plane (1) are 2, –2, 4,
Direction ratios of normal to plane (2) are 3, – 3, 6.
Now, 
∴ given planes (1) and (2) are parallel.
