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It is quite normal for a person to wonder if one can apply the methods of division on a pair of vectors similar to the other mathematical operations. However, the answer to that question just might not be what you are looking for. We can add, subtract and multiply two vectors, however, the same can not be said for the method of division. This method does not apply to two vectors. Even if it can be applied to a certain pair of vectors, this method will never be able to turn into anything universal.
Why is there no division of vectors?
There is known to be no proper division of vectors because there is no particular need for it. All the operations that are included in the vectors are addition, subtraction and multiplication. It follows the principle that when we add two vectors, we get a vector; when we subtract two vectors we get a vector; when we multiply two vectors, we get a vector. However, the same can not be said for the case of division.
In the case of division, it is clear that the vector will end up losing all of its units. And, besides it is clear that when a vector is divided by the same vector the outcome will be 1→. And, it is clear that the vector of 1 does not have a specified value.
On the other hand, it is also possible to define the division of two vectors, by using the multiplication of one vector with the inverse of another. If that is the case, then there is absolutely no need for the division of vectors. Therefore, there is no particular need for us to find out the division of two vectors. We can use other operations to define that function.
What is the quotient of two vectors?
The geometric entity that is the quotient of two vectors is referred to as the quaternion of those vectors. This is the entity that is obtained when one vector is divided by another vector. However, it is said that the division of two vectors is not defined, but it still holds an appropriate counter to support the following statement.
The division of two vectors giving quaternion, as a result, does not stand true for all the vectors that are chosen. There are a specified number of vectors for which this kind of relationship can be proven. All the vectors do not support the characteristics to be able to be divided by one another, hence they must carry a natural operator that can be divided.
Using this principle, it is possible to find the division for vectors that are present in 2D and 4D geometry, but the same can not be said for 3D vectors. This principle carries its own set of properties and follows only a set of well-defined algebraic operations. Hence, it is possible to get the outcomes out of this. Hence, it can be said that there is no proper way to find the division of vectors. However, in certain cases, it is possible to do so.
What is vector division?
It is strictly forbidden for us to consider the division of two vectors ad the division of the coefficients of the direction of that vector. This is a result that will never stand true for any pair of vectors. This interpretation is nothing else but a misunderstanding.
This is no such method introduced for the division of two vectors that utilize the division of coefficient of direction ratios of a vector with another. This result will not be supported in any way by a pair of vectors.
Only the method of quaternions is known to help us get the division of two vectors. However, even that method is not full-fledged. This method is not used for every pair of vectors that can be put into question. This method is applicable only for a certain group of vectors, and it helps us in deriving the properties of those vectors.
Conclusion
The result of the division of two vectors is not a concrete one. However, we can reach an outcome if we take the concept of quaternions into account. Using this method, we can divide a vector by another. However, this method is not universal. It is applicable only for a certain set of vectors. Besides those, we can’t find out the division of the two vectors. Hence, the concept of vector division also carries significant importance.
