How are two vectors collinear

Parallelism, Collinearity, and Complanarity (Vector)

Some important terms of vector calculation are to be clarified in this mathematics article. Afterwards you should know what is hidden behind the terms parallelism, anti-parallelism, collinearity and planarity.

Before we start with some important terms in vector calculation, it would be good if you already have some knowledge of vectors. So if you don't know what a vector is, please read the following articles first:


Equality, parallelism and anti-parallelism

Let's start with the term "equality" in terms of vectors. The following applies: Two vectors are said to be the same if they match in length and direction. The following two vectors are "equal":

Table scrollable to the right

Let us come to the parallelism of vectors: Two vectors with the same direction are said to be parallel to each other. The graphic below shows two parallel vectors:

Table scrollable to the right

The anti-parallel vectors are still missing. This can be defined as follows: If two vectors have opposite directions, they are referred to as being anti-parallel to one another. The graphic below shows two anti-parallel Vectors:

Table scrollable to the right

Collinear and Complanar

Collinear vectors are parallel or anti-parallel vectors. One of the two vectors is a multiple of the other vector. The following example shows two collinear vectors.

Finally we consider the coplanar vectors. This is understood to mean vectors that lie in one plane. Unfortunately, this is a fairly extensive topic. For this reason, reference is made to other chapters of the vector calculation that deal with the topic of plane calculation.


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