skew lines: meaning, definition, pronunciation and examples
C1Technical/Academic
Quick answer
What does “skew lines” mean?
Two straight lines in three-dimensional space that are not parallel and do not intersect.
Audio
Pronunciation
Definition
Meaning and Definition
Two straight lines in three-dimensional space that are not parallel and do not intersect.
In geometry, lines that lie in different planes and never meet, representing the most common relative position of two lines in 3D space. In figurative use, it can describe ideas, paths, or processes that proceed in completely different directions without converging.
Dialectal Variation
British vs American Usage
Differences
No significant difference in technical meaning. The term is equally standard in both mathematical communities.
Connotations
Neutral technical term in both varieties. Sometimes used metaphorically in academic or managerial contexts to describe diverging strategies or non-interacting systems.
Frequency
Low frequency in general discourse, high frequency in specific STEM fields (mathematics, engineering, physics, computer graphics).
Grammar
How to Use “skew lines” in a Sentence
Lines L1 and L2 are skew.To prove that two lines are skew.The lines are skew to each other.A line skew to a given plane.Vocabulary
Collocations
Examples
Examples of “skew lines” in a Sentence
adjective
British English
- The two support rods are in a skew arrangement.
- We need to calculate the shortest distance between the skew cables.
American English
- The two support rods are arranged skew to each other.
- The engineer analyzed the skew conduits running through the ceiling plenum.
Usage
Meaning in Context
Business
Rare. Potentially metaphorical: 'The marketing and R&D departments are on skew lines—they never truly communicate.'
Academic
Core concept in geometry, linear algebra, and technical drawings. Used in proofs and spatial reasoning problems.
Everyday
Extremely rare. Would only be used by someone describing a specific 3D spatial relationship.
Technical
Fundamental. Used in mathematics, engineering (e.g., specifying the position of beams or wires in space), computer-aided design (CAD), and 3D modeling.
Vocabulary
Synonyms of “skew lines”
Neutral
Weak
Vocabulary
Antonyms of “skew lines”
Watch out
Common Mistakes When Using “skew lines”
- Using 'skew lines' to describe lines in a 2D plane. (They must be in 3D space.)
- Confusing 'skew' with 'oblique'. (All skew lines are oblique relative to each other, but 'oblique' is broader and can describe angles in 2D.)
- Pronouncing 'skew' as /skuː/ instead of /skjuː/.
FAQ
Frequently Asked Questions
No. By definition, skew lines exist only in three-dimensional (or higher) space. In a 2D plane, any two non-parallel lines will always intersect.
The shortest distance is the length of the line segment that is perpendicular to both lines. This segment is unique for a given pair of skew lines.
No. Train tracks on level ground are a classic example of parallel lines. For them to be skew, one track would have to be on a bridge and the other on the ground below, running in a different direction.
You must prove two things: 1) The lines are not parallel (their direction vectors are not scalar multiples). 2) The lines do not intersect (there is no single point that satisfies the parametric equations of both lines).
Two straight lines in three-dimensional space that are not parallel and do not intersect.
Skew lines is usually technical/academic in register.
Skew lines: in British English it is pronounced /skjuː laɪnz/, and in American English it is pronounced /skjuː laɪnz/. Tap the audio buttons above to hear it.
Learning
Memory Aids
Mnemonic
Imagine two vapour trails in the sky from aeroplanes flying at different altitudes and in different directions. They are not parallel, and because they are at different heights, they will never cross. They are skew lines in the 3D space of the sky.
Conceptual Metaphor
DIVERGING PATHS (two entities developing independently without ever meeting or directly interacting).
Practice
Quiz
Which of the following best describes skew lines?