No, lines of latitude do not intersect.
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always. if two lines intersect, then exactly one plane contains the lines.
Coplanar lines that don't intersect are parallel. Lines that are not parallel and do not intersect are skew lines.
no they are straight lines that never intersect, intersecting lines intersect.
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.