Q: Are Two skew lines are always parallel?

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No, not always. Skew lines are never coplanar, but parallel lines are.

A line and a plane that do not intersect are always skew. Skew refers to two or more lines or planes that are not parallel and do not intersect. Since a line and a plane are different-dimensional objects, they will never intersect and will always be skew.

Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.

Parallel Lines - Skew lines are lines that do not intersect and do not lie in the same plane. If two lines lie in the same plane they they must either intersect or they are parallel.

They could be if they are both skew to the same line.

Related questions

No, not always. Skew lines are never coplanar, but parallel lines are.

Two lines that are not parallel and do not intersect are skew. If the non-intersecting lines are in the same plane then they are parallel.

Two lines in two intersecting planes can be parallel, intersecting, or skew.

Skew lines

Skew lines

Parallel Lines or Skew Lines.

A line and a plane that do not intersect are always skew. Skew refers to two or more lines or planes that are not parallel and do not intersect. Since a line and a plane are different-dimensional objects, they will never intersect and will always be skew.

Each line can either intersect the edge which is common to the two planes at some point or be parallel to it. If the two lines intersect the edge, but at different points, then the lines are skew. If only one of the lines intersects the edge, then again the lines are skew. If neither of them intersect, then the two lines are parallel to the same edge and so they are parallel to one another so not skew.

Parallel Lines - Skew lines are lines that do not intersect and do not lie in the same plane. If two lines lie in the same plane they they must either intersect or they are parallel.

They could be if they are both skew to the same line.

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.

Skew lines never intersect. If two lines intersect, then they are known as "intersecting lines", not skew lines.