Not necessarily. If two rays are on different planes, but the planes intersect, it is possible that the rays would also intersect, but the plane intersection would have to happen where the rays are located.
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Two lines of a plane are said to be parallel if they do not intersect and the perpendicular distance betweem them is always same.
parallel lines If they are not on the same plane and never intersect they are skew
Lines which are parallel. All other lines on the same plane eventually intersect.
If they are not parallel and do not intersect then they would not be in the same plane (not possible), but they would be called skew lines.
No, if the lines were in the same plane they would be parallel and never intersect