Noncoplanar lines that do not intersect are
considered to be skew lines.
called skew lines. Skew lines are a pair of lines that are not parallel and do not lie in the same plane, which means they cannot intersect or be coplanar. Unlike parallel lines, skew lines do not have any points in common, and they continue indefinitely without ever crossing each other.
called skew lines. Skew lines are two or more lines that are not in the same plane and do not intersect. In other words, they are neither parallel nor intersecting. To determine if lines are skew, you need to check if they lie in different planes and do not intersect.
To determine if lines are coplanar or not, you can use the vector equation of the lines and check if there is a common point of intersection. If the lines have a common point of intersection, then they are not skew. However, if the lines do not have a common point of intersection and lie in different planes, then they are skew.
For example, let's consider two lines in three-dimensional space with their vector equations:
Line 1: r = a + t1 * u
Line 2: r = b + t2 * v
Here, a and b are position vectors of a point on each line, and u and v are direction vectors of the lines. t1 and t2 are parameters that can vary.
To check if the lines are skew, you can set up a system of equations:
a + t1 * u = b + t2 * v
If this system of equations has no solution, then the lines are skew because they do not intersect. On the other hand, if a solution exists, then the lines intersect and are not skew.
Keep in mind that skew lines are only possible in three-dimensional space. In two-dimensional space, lines are either parallel or intersecting.