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Intersecting Lines are Skew

TopThe lines which do not intersect, they are not parallel as well and which are not coplanar are known as skew lines. Now the question arises that the Intersecting Lines are skew or not?

By definition of skew lines we can say that skew lines never intersect each other and also not parallel.

For example: Regular tetrahedron is best example of skew lines, it is composed of four triangular faces, out of all faces three faces of regular tetrahedron meet at same Point. The lines which are coplanar either intersect or are parallel, so we can say that the skew lines exist in three or more dimensions.

Now we will see how to find the distance between two skew lines:

Here we use formula for finding the distance between two skew lines:

=> x = P + ⋋Q; and

=> y = R + uS;

And the cross product of ‘Q’ and ‘S’ is perpendicular to the lines, as is the unit vector.

$\frac{Q \times S}{|Q \times S|}$

If the values of |Q * S| is zero then the lines are parallel and this method cannot be used, then the formula for finding the distance between two lines is:

D = | n. (R - P) |,
In pair of skew lines each line is defined by two points, so these are not coplanar.
Now we will see the configurations of multiple skew lines:
Set of lines in which the given pair is skewed is said to be configuration of skew lines. If two configurations are possible to transform one configuration to another then the two configurations is said to be isotopic and any of the two configurations can be isotopic.