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

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

2 × 1 + 1 × (-2) + 3 × 0

= 0

Thus, the given planes are ⊥ to each other.

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