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Coinitial Vectors

Coinitial vectors are defined as two or more vectors in algebra whose initial points are the same, that is, they start at the same point. Co initial vectors may or may not parallel vectors. They can be intersecting vectors or parallel vectors depending upon the direction of the vectors. In other words, we can say that any two or more given vectors are said to be co initial vectors if they have the same initial points.

Further in this article, we will explore the concept of coinitial vectors, the definition of co initial vectors, and the difference between the coinitial vectors and collinear vectors. We will also solve a few examples based on the concept for a better understanding of the concept.

1.	What are Coinitial Vectors?
2.	Co Initial Vectors Definition
3.	What are Co initial Vectors and Collinear Vectors?
4.	FAQs on Coinitial Vectors

What are Coinitial Vectors?

Two or more vectors are said to be co initial vectors if they have the same initial point. Such vectors start at the same point. It is not necessary for the coinitial vectors to have the same terminal point, they must have the same initial point. Coinitial vectors can be parallel or intersecting vectors. Two vectors \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) are co initial vectors as they have the same initial point A. Both vectors \(\overrightarrow{AB}\) and \(\overrightarrow{AC}\) have the same starting point but their terminal points are different. Let us define the coinitial vectors in the next section.

Co Initial Vectors Definition

Co initial vectors are defined as two or more vectors in vector theory that have the same initial point. In simple words, we can say that coinitial vectors have the same starting point. The image given below shows five vectors, namely OA, OB, OC, OD, and OE. The one thing common in all these five vectors is that they all start at the same point which is O. Hence, vectors OA, OB, OC, OD, and OE are coinitial vectors with the initial point O.

Coinitial vectors

What are Co initial Vectors and Collinear Vectors?

In this section, we will understand the meaning of coinitial vectors and collinear vectors. Two or more vectors that start from the same initial point are said to be coinitial vectors. On the other hand, two or more vectors are said to be collinear vectors if they are parallel to the given same line. Let us now understand the differences between the co initial vectors and collinear vectors:

Coinitial Vectors Vs Collinear Vectors

Co initial Vectors	Collinear Vectors
Two or more vectors are said to be coinitial vectors if they have the same initial point.	Two or more vectors that are parallel to the same given line are said to be collinear vectors.
Co initial vectors may be parallel or intersecting.	The ratio of the coordinates of two collinear vectors is constant.
Vectors OA and OB are coinitial vectors as they have the same initial point O.	If vectors p, q are collinear, they can be expressed as p = nq, where n is a scalar.

Important Notes on Coinitial Vectors

Vectors that have the same starting point are said to be coinitial vectors.
Two or more vectors that are parallel to the same given line are said to be collinear vectors.
Co initial vectors can be intersecting vectors or parallel vectors depending upon the direction of the vectors

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Coinitial Vectors Examples

Example 1: Find if the given vectors OA = 2i + j and OB = 5i + j are coinitial vectors.

Solution: In a vector notation, the first letter indicates the initial point of the vector. For example, in vector AB, A is the initial point and B is the terminal point.

So, in vectors OA and OB, the initial point is the same which is O.

Hence, these vectors are co initial vectors.

Answer: OA and OB are coinitial vectors
Example 2: Check if the vectors AB and BC are co initial vectors.

Solution: For any arbitrary vectors AB and BC, the initial point for vector AB is the point A, and its terminal point is B.

Similarly, for vector BC, the initial point is B and the final point is C. As we can see, the initial points for the two vectors AB and BC are not the same, hence AB and BC are not collinear provided point A is not equal to point B.

Answer: The vectors AB and BC are not co initial vectors.

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Coinitial Vectors Questions

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FAQs on Coinitial Vectors

What are Coinitial Vectors in Vector Theory?

Coinitial vectors are defined as two or more vectors in algebra whose initial points are the same, that is, they start at the same point. These vectors can be parallel or intersecting vectors.

How to Identify Coinitial Vectors?

If two or more vectors have the same starting point, that is, they start from the same point, then the vectors are said to be co initial vectors. In other words, we can say that we can identify the coinitial vectors if they have the same initial point.

What is the Difference Between Co initial Vectors and Collinear Vectors?

Vectors that have the same initial point are said to be co initial vectors. On the other hand, vectors that are parallel to the same given line are called collinear vectors. Collinear vectors can be expressed as the p = nq, where n is a scalar and p, q are collinear vectors.

What is the Difference Between Co Initial Vectors and Coplanar Vectors?

Co initial vectors are defined as two or more vectors in vector theory that have the same initial point. On the other hand, vectors that lie on the same plane in a three-dimensional space are said to be coplanar vectors.

What are Coterminous Vectors?

Two or more vectors that have the terminal point, that is, have the same endpoint or final point are called coterminous vectors.

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