Equation of Plane Containing Point (-1,2,-2) & Satisfying Conditions

[popo902]

Homework Statement

write the equation of the plane that contains the point(-1, 2, -2) and satisfies
1. parallel to xy plane
2. orthogonal to z-axis
3.parallel to both the x and z axes
4. parallel to the plane x-y+3z = 100 (plane A)

Homework Equations

The Attempt at a Solution

i started with finding the normal of plane A which is <1,-1,3>
and i know that the normal of this plane should be the normal of my plane suince they're
parallel
but what i don't get is how the plane I am finding can be orthogonal the the z axizs and parallel to it at the same time...
i drea it and it still doesn't look like it makes sense
i don't know where to go from here...

 

[rock.freak667]

i started with finding the normal of plane A which is <1,-1,3>
and i know that the normal of this plane should be the normal of my plane suince they're
parallel
but what i don't get is how the plane I am finding can be orthogonal the the z axizs and parallel to it at the same time...
i drea it and it still doesn't look like it makes sense
i don't know where to go from here...

Are you sure you don't need to find planes for each of the conditions? I don't think there is a single plane that satisfies all of those conditions.

 

[Mark44]

The first two equations are equivalent. A plane that is parallel to the x-y plane is automatically orthogonal to the z-axis.

 

[popo902]

now that i think of it...i think i was supposed to find ones that satisfy each.
wow i feel dumb
i was actually stressing about how a plane could bend to meet the reqs :s