The information supplied in the question is confusing. Is the one plane and a line or two lines and two planes - or some other combination? Please edit the question to include more context or relevant information.
They are skew lines. Two parallel lines must be in the same plane.
They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.
Coordinate Plane
A square...!?!
Parallel lines would always lie in the same plane. They would need to be skew lines.
Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect Lines in the same plane that do not intersect
Think about it, the x & y planes intersect and what one number has both, the x & y planes intersect. 0 on the coordinate plane is the, origin.
Skew lines, which live in parallel planes.
A two dimensional plane.
They are skew lines. Two parallel lines must be in the same plane.
They are called skew lines. Explanation: In 3 space, parallel lines must never intersect AND must be in the same plane. If they fail to intersect and are in different planes we call them skew lines.
Coordinate Plane
No, two planes do not intersect in exactly one plane unless the planes are exactly overlapping, making one plane. In Euclidean Geometry two planes intersect in exactly one line.
A square...!?!
a coordinate plane
Two planes that intersect are simply called a plane to plane intersection. When they intersect, the intersection point is simply called a line.
Parallel lines would always lie in the same plane. They would need to be skew lines.