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There is no such thing as a skew plane - in isolation. It can only be skew with reference to something else.
No. Skew lines do not intersect
Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.
In linear algebra, a skew-symmetric matrix is a square matrix .....'A'
Correct! Skew lines can never by be parallel.