In the following cases, determine whether the given planes are parallel or perpendicular, and in case they are neither, find the angles between them.
7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
The eq. of the given planes are
7x + 5y + 6z + 30 = 0 and 3x – y – 10z + 4 = 0
Two planes are ⊥ if the direction ratio of the normal to the plane is
a1a2 + b1b2 + c1c2 = 0
21 – 5 – 60
-44 ≠ 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
13