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 + y + 3z – 2 = 0 and x – 2y + 5 = 0
The eq. of the given planes are
2x + y + 3z – 2 = 0 and x – 2y + 5 = 0
Two planes are ⊥ if the direction ratio of the normal to the plane is
a1a2 + b1b2 + c1c2 = 0
2 × 1 + 1 × (-2) + 3 × 0
= 0
Thus, the given planes are ⊥ to each other.