Skew Lines in 3D
Since skew lines are inherently non-coplanar, they will always exist in three dimensions.
Assume the following three-dimensional solid shape as shown in the image below. On the triangle face, we draw a single line that we call “a.” We designate ‘b’, the single line that we draw on the quadrilateral-shaped face.
There isn’t a plane that contains both a and b. “a” and “b” are not parallel to one another and will never intersect if we stretch them indefinitely in both directions. Thus, in 3D, “a” and “b” are skew lines.
Skew Lines
Skew Lines: Skew lines refer to a pair of lines that neither intersect nor run parallel to each other. This concept only applies in spaces with more than two dimensions, as skew lines must reside in separate planes, making them non-coplanar. In contrast, within two-dimensional space, lines are limited to two relationships: they can either cross each other or be parallel.
In this article, we will learn about skew lines, examples of skew lines, and how to calculate the shortest path between skew lines and other details.
Table of Content
- What are Skew Lines?
- Skew Lines Definition
- Skew Lines Examples
- Skew Lines in 3D
- Skew Lines in a Cube
- Skew Lines Formula
- Angle Formed by Two Skew Lines
- Formula for Distance Between Skew Lines
- Vector Form
- Cartesian Form
- Distance Between Skew Lines
- Distance Between Two Skew Lines
- Shortest Distance Between Two Skew Lines
- Notes on Skew Lines
- Solved Examples on Skew Lines
- Practice Problems on Skew Lines