Final answer:
To determine if planes are parallel or perpendicular, analyze their normal vectors. The first plane's normal vector is (1, -1, -9), but the second plane's equation appears incorrect and needs to be in the form Ax + By + Cz = D to determine its normal vector.
Step-by-step explanation:
To determine if the planes x - y - 9z = 1 and 9xy - z = 3 are parallel, perpendicular, or neither, we need to look at the normal vectors of each plane. For the first equation, the normal vector would be (1, -1, -9). However, the second equation is not correctly written in the plane form. A plane should have the form Ax + By + Cz = D. Assuming there is a typo and the correct equation might be something like 9x - y - z = 3, then the normal vector for this plane would be (9, -1, -1). Two planes are parallel if their normal vectors are scalar multiples of each other, and they are perpendicular if their dot product is zero. Here, without the correct second equation, we cannot determine the relationship. Please provide the correct form of the second plane equation for a complete answer.