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Never! Coplanar means that the two lines lie in the same two-dimensional plane. The only way that two lines do not intersect in two-dimensional space is if they are parallel. And by definition, skew lines are not allowed to be parallel, either.

So essentially there is no such thing as skew lines that only occupy two dimensions. Skew lines must be in three dimensions or higher in order to (1) not intersect and (2) not be parallel with each other.

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Q: When are skew lines coplanar?
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