Collinear Vs Parallel Vectors
Parallel vectors are specific case of collinear vectors. Some other differences between collinear vectors and parallel vectors are listed in the following table:
| Feature | Collinear Vectors | Parallel Vectors |
|---|---|---|
| Definition | Vectors that lie along the same line | Vectors that have the same or opposite direction |
| Direction | May have the same or opposite direction | Always have the same or exactly opposite direction |
| Mathematical Relation | u =kv for some scalar k. | u = kv for some scalar k, k > 0 for same direction, k < 0 for opposite |
| Example | u = (1,2), and v = (2,4) | u =(3, 3), v =(−6,−6) (opposite direction) |
| Geometric Interpretation | Vectors that can be scaled to overlap when plotted from a common point | Vectors that are either exactly aligned or directly opposite when plotted from a common point |
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Collinear Vectors
Vectors are also called Euclidean vectors or Spatial vectors, and they have many applications in mathematics, physics, engineering, and various other fields. There are different types of vectors, including zero vectors (which have 0 magnitude and no direction), unit vectors (which have a magnitude of 1), position vectors, co-initial vectors, like and unlike vectors, co-planar vectors, collinear vectors, equal vectors, displacement vectors, and negative vectors.
In this article, we will discuss collinear vectors and the criteria according to which two vectors are said to be collinear in detail.
Table of Content
- What are Vectors?
- What are Collinear Vectors?
- Conditions for collinearity of vectors
- Collinear Vs Parallel Vectors
- Solved Examples
- Practice Problems
- FAQs: Collinear Vectors