Determine whether the planes are parallel, perpendicular, or neither. x − y − 3z = 1, 3x + y − z = 2
If neither, find the angle between them. (Round your answer to one decimal place. If the planes are parallel or perpendicular, enter PARALLEL or PERPENDICULAR, respectively.)

Neither planes are parallel nor perpendicular to each other. (NEITHER)

Step-by-step explanation:

Each expression can be represented as dot product, that is:

Where first vector is known as plane generator. It is also known that dot product equals to the following expression:

The cosine is therefore cleared:

The norm of each vector is determined by these expressions:

and

Planes are parallel to each other when and perpendicular to each other if .

If and , then:

Neither planes are parallel nor perpendicular to each other.

n

step-by-step explanation: