A line segment can be defined as having two endpoints
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No. The planes must either coincide (they are the same, and intersect everywhere), be parallel (never intersect), or intersect in exactly one line.
Yes. In fact, if they are not the same plane, then they must intersect in a unique straight line.
Not only must they intersect, but they must be parts of the same line.
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.
They are skew lines. Two parallel lines must be in the same plane.