# Translation or parallel movts of vectors

• phyeinstein_c
In summary, the conversation discusses the concept of vectors and their translation and movement in relation to rigid bodies. The terms "bound vectors" and "free vectors" are introduced to describe vectors with specific initial points and those with only magnitude and direction. The conversation also touches on the relationship between velocity and torque, as well as the mathematics of vectors in Euclidean space. There is some confusion about the terminology and application of these concepts, but ultimately it is agreed that vectors can be translated and moved around in different ways.

#### phyeinstein_c

my teacher says that vectors can be translates which is fine... but homework can they be moved paralaly without couple acting on it//??

hi phyeinstein_c!
phyeinstein_c said:
my teacher says that vectors can be translates which is fine... but homework can they be moved paralaly without couple acting on it//??

i think you're confusing a bound vector with a free vector (i've forgotten the correct names, but it's something like that ) …

force is a bound vector, and so its line of application has to be included when specifying it

velocity is a free vector, and you can shove it around so as to put it on the end of another vector

so free vectors do translate, but bound vectors like force (as you say) don't

but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??

hi phyeinstein_c!
phyeinstein_c said:
but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??

hmm, let me think

yes, a force vector certainly generates torque (and a momentum vector generates angular momentum , and momentum is simply mass times a velocity vector ) …

perhaps i should have said that relative velocity is a free vector, and you can shove it around so as to put it on the end of another vector!

but if velocity vector mover parallaly from one end of a rigid body (not point mass) then it generates torque right??

This statement is nonsense.

First, if one part of a rigid body possesses a certain velocity (vector) then all parts posess the same vector. That is a definition of a rigid body.

So velocity vectors cannot move around a rigid body willy nilly.

Second, velcocity cannot produce torque under any circumstances. That is the province of forces or couples.

Tinytim has already said that force is a bound vector, which means you cannot move it about. What he did not say is that bound vectors also have an origin or point of application as part of their specification.

So if you change the point of application of a force, yes you will induce different moments in a rigid body.

Finally for the record couples are free vectors which may be moved about.

ok sry by torque i meant rotation... velocity will be uniform is a case... but when the vector has been taken to one end of the body.. it shud rotate...couple will act only for forces right.

phyeinstein_c said:
ok sry by torque i meant rotation... velocity will be uniform is a case... but when the vector has been taken to one end of the body.. it shud rotate...couple will act only for forces right.

What do you mean?

i mean when the velocity vector is shifted from the centre to one end... parallally... the body has higher velocity on one end and less on the other... so it should rotate...??

Let us start again at the beginning.

What system are you describing?

a mathematician will not understand a word you guys are saying. mathematically a vector in Euclidean space is an equivalence class of parallel arrows all with same direction and magnitude, and all having different endpoints. Any one of those arrows represents the vector. In that sense we say vectors can be translated. Some say more abstractly that a vector IS a translation of space, and is represented by the arrow drawn from any point to its translated image.

In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

I chime in here because i thought maybe your teacher is a mathematician and does not know what you are talking about either.

In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

Yup that's about it (I'm well known for my precise mathematical statements ).

hi mathwonk!
mathwonk said:
In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

i'm sorry to disillusion you, but wikipedia has heard of them, see http://en.wikipedia.org/wiki/Euclidean_vector" [Broken] …

As an arrow in Euclidean space, a vector possesses a definite initial point and terminal point. Such a vector is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.​

(though it then seems to get lost, see http://en.wikipedia.org/wiki/Euclidean_vector#In_Cartesian_space" )

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Studiot said:
Let us start again at the beginning.

What system are you describing?

its a rigid body translating...

mathwonk said:
a mathematician will not understand a word you guys are saying. mathematically a vector in Euclidean space is an equivalence class of parallel arrows all with same direction and magnitude, and all having different endpoints. Any one of those arrows represents the vector. In that sense we say vectors can be translated. Some say more abstractly that a vector IS a translation of space, and is represented by the arrow drawn from any point to its translated image.

In applying the concept you may wish to distinguish between an individual arrow, and the class it represents. maybe this is what you call free and bound vectors, but i have never heard of them.

I chime in here because i thought maybe your teacher is a mathematician and does not know what you are talking about either.
neither did i ever hear of such bounded vectors... in any VECTOR by definition its only REPRESENTATION of magnitude and direction... homework does it matter if it is bounded or unbounded or free...

tiny-tim said:
hi mathwonk!

i'm sorry to disillusion you, but wikipedia has heard of them, see http://en.wikipedia.org/wiki/Euclidean_vector" [Broken] …

As an arrow in Euclidean space, a vector possesses a definite initial point and terminal point. Such a vector is called a bound vector. When only the magnitude and direction of the vector matter, then the particular initial point is of no importance, and the vector is called a free vector.​

(though it then seems to get lost, see http://en.wikipedia.org/wiki/Euclidean_vector#In_Cartesian_space" )
can u discuss some cases (examples) of the 2 cases u metioned..

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in any VECTOR by definition its only REPRESENTATION of magnitude and direction

No there is more to it than just magnitude and direction.

Suppose I started in London and traveled 300 mile due north, turned and then traveled 300 miles due west.

Now suppose I did it the other way around ie 300 miles west then 300 miles north.

Would I be in the same place the second time around?

It is an important, and not often stated, requirement that

vector(a) + vector(b) = vector(b) + vector(a)

This is another way of saying that a+b is given by the parallelogram law.

ohkk that's there but how does it matter in physics... the result of both is u have had the same displacement and u will have the same velocity etc. during both kind of journey.

ohkk that's there but how does it matter in physics... the result of both is u have had the same displacement and u will have the same velocity etc. during both kind of journey.

Since the English was so mangled I have no idea what you mean.

"Would you end up in the same place either way?"

## 1. What is translation or parallel movement of vectors?

Translation or parallel movement of vectors is the process of moving a vector from one position to another without changing its magnitude or direction. This is done by adding or subtracting a constant value to the x and y coordinates of the vector.

## 2. How is translation different from rotation of vectors?

Translation involves moving a vector in a straight line, while rotation involves changing the direction of the vector by a certain angle. In translation, the magnitude of the vector remains the same, while in rotation, both the magnitude and direction can change.

## 3. Can translation be applied to any type of vector?

Yes, translation can be applied to any type of vector, whether it is a geometric vector (represented by arrows) or a mathematical vector (represented by ordered pairs or coordinates).

## 4. What is the purpose of translation in mathematics?

Translation is used in mathematics to study and analyze the movement of objects in space. It is also used in geometry to determine the properties and relationships of translated figures.

## 5. How is translation useful in real life applications?

Translation is useful in various real life applications, such as computer graphics, animation, and engineering. It is also used in navigation systems to determine the position of objects or vehicles in relation to a reference point.