No. Skew lines do not intersect
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Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
No, skew lines are not perpendicular. Perpendicular lines intersect at an angle of ninety degrees, while skew lines never intersect (think in three dimensions or higher).
No, skew lines cannot be in the same plane, since they do not have a point on common. Two lines intersect if they lie in a common plane, and by definition, these intersecting lines are not skew lines.
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
Skew lines.