- #1
PhyHunter
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Can we divide two vector ? If we can't why
divison when [tex said:d,e,f\neq 0[/tex] :
[tex](a,b,c)/(d,e,f)=(a/d,b/e,c/f)[/tex]
Obviously, you will see this popping up in Functional Analysis, which is a generalization of linear algebra.
PhyHunter said:How do you prove it ?
MathematicalPhysicist said:Obviously, you will see this popping up in Functional Analysis, which is a generalization of linear algebra.
Well, you can check the subject of Banach Algebras, I first encoutered this subject in the second course in Functional analysis which was given at my school.
PhyHunter said:Can I say something.In matrices (2x1)/(2x1)=(2x2) we can say this because If we want to control that we must multiply (2x2)x(2x1) and we get (2x1) so I understand that a/b question's answer is two vector system.Can we say this ?
(HERE a and b vector) and (2x1) or (2x2) is matrices)
( (2x1) matrice symbolize vector)
In words: the product of a 2 x 2 matrix and a 2 x 1 matrix is a 2 x 1 matrix.PhyHunter said:Sure,we symbolize vector in matrix (2x1) so If we try divide two vectors in matrix system, (2x1)/(2x1) we get (2x2) so if we want control this,we will multiply (2x2)x(2x1) and we get (2x1)
(2x1) is one vector (2x2) is two vector system
[tex](2x2)x(2x1)=(2x1)[/tex]
I don't see how this makes sense. Matrix multiplication is defined if the multiplication is conformable. IOW, AB makes sense if the number of columns of A is the same as the number of rows of B.PhyHunter said:so we can say
[tex](2x1)/(2x1)=(2x2)[/tex]
PhyHunter said:If we want write this in vector system
pointwise of vectors
[tex](a,b)/(c,d)=((a/c,0),(0,b/d))[/tex]
or [tex]a/b=((c,d))[/tex]
(a,b,c,d) vectors
Vector division is an operation in which a vector is divided by another vector, resulting in a new vector. It is a mathematical operation that combines the magnitude and direction of two vectors to create a new vector.
The main difference between vector division and scalar division is that vector division results in a vector, while scalar division results in a single number. Vector division also takes into account the direction of the vectors, while scalar division only considers their magnitudes.
There are several properties of vector division, including associativity, commutativity, and distributivity. Vector division is associative, meaning that the order of the vectors being divided does not affect the result. It is also commutative, meaning that the order of the vectors can be switched without changing the result. Finally, vector division follows the distributive property, which means that it can be distributed over vector addition and subtraction.
No, vector division is only defined for vectors in the same direction. In order to divide two vectors, they must be parallel or collinear. If the vectors are not parallel, vector division is not possible.
Vector division is commonly used in physics and engineering, such as calculating the velocity and acceleration of objects in motion. It is also used in navigation, for example, in determining the direction and speed of a plane or ship. Additionally, vector division is used in computer graphics to create 3D images and animations.