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Old Apr 23rd 2018, 08:41 AM   #1
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What is the difference between a vector and a scaler in 1 dimension.

Lets say we have -10 as a vector and we have a scalar also having value -10 in one dimension. So whats the difference?
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Old Apr 23rd 2018, 08:52 AM   #2
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Answer.

I think I have the answer to it. If suppose the -10 in our example is -10 metres, which means there is a unit attached to it which is metres then its a vector and just -10 without the units would mean its a scalar.
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Old Apr 23rd 2018, 09:04 AM   #3
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Clarification.

Now let us consider we multiply the scalar temperature to velocity. We all know that temperature is a scalar quantity. Lets say we have -5 degrees celcius and we multiply it with 20 m/s North.

Now the answer is -100 celcius m/s North. Here as per my understanding the sign - as in -5 celcius does not define the direction it is only quantity. All what it means is that the object is -5 degrees celcius more than the freezing point of water which is 0 degrees celcius.

So the direction is North again which hasnt changed. So with this example we know the direction of the vector hasnt changed.

I would like to request you examples where when scalar is multiplied to a vector the direction has changed. Can you give any such examples?
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Old Apr 23rd 2018, 09:30 AM   #4
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I can see the sense in saying that a scalar and a one dimensional vector are synonymous.
However, I am sure that pure mathematicians would disagree.
It is probably a moot point, of more philosophical than practical importance.

I disagree with your suggestion that the units make the difference.

With regard to your temperature & speed example,
you can't just take random, unrelated, values and combine them in an equation,
the result simply has no meaning.

A scalar does not change the direction of a vector, that is a fundamental feature of the definition of these mathematical constructs.

I have seen topsquark posting that changing the sign of the vector by scaling by a negative scalar is changing the direction.
Again this is probably a moot philosophical point for pure mathematicians,
but I would say this this is still a change of scale rather than a change of direction.
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Old Apr 24th 2018, 05:24 AM   #5
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What is the difference between a vector and a scaler in 1 dimension.
This can be very confusing when you start so it is a good idea to get a firm grip on the words.

There is no such thing as a one dimensional vector in Physics.

All vectors have at least two components corresponding to at least two dimensions.

That is there are two variables that can be varied independently of each other, over the full range of available numbers or scalars.

This requirement for variability over the full range is why +1/-1 are not acceptable and direction meaning just forwards and backwards is not acceptable as a vector.


This distinction is of little consequence in ordinary everyday common or garden vectors.

But it becomes vitally important when you move on to study tensors.

Tensors have something called rank, rather than dimension.

The theory of tensors fills in the awkward spots in vector theory and answers some of these questions.
This is because tensors are also defined as transforming according to certain rules.

One of these rules of transformation is that scalars are unchanged by a transformation.

Examples of this are

Both temperature and frequency are measured as a simple single number.

Temperature is a scalar, but frequency is not a scalar.

You will measure the temperature of a body the same, regardless of whether you are standing next to that body or moving towards it or away from it.

Temperature transforms from the standing still to the moving situation according to the equation

T' = T

Where T is the temperature in the standing still coordinate system and T' is the temperature in the moving one.


But the same cannot be said for the frequency of a wave emitted by that body.
This changes according to the motion by a much more complicated equation.

T' = T is one definition of a scalar ( as opposed to just a number).

In this scheme scalars are defined as tensors of rank zero, and vectors are defined as tensors of rank 1.
As such all the scalar - vector arithmetic works well.
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Last edited by studiot; Apr 24th 2018 at 06:21 AM.
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Old Apr 24th 2018, 08:32 AM   #6
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Originally Posted by avito009 View Post
Lets say we have -10 as a vector and we have a scalar also having value -10 in one dimension. So whats the difference?
The difference is that a vector has a unambiguous direction whereas a scalar only has a value, in this case -10. -10 can have a location along a curve, such as along a coordinate axis but not a direction Now suppose that you define the direction by the sign of the scalar and its magnitude as the magnitude of the vector. That is still insufficient. Is it pointing in he -z, -y or - z direction? If you then specify that then in effect you're defining a direction. But to make it a real vector instead o your own creation which will upset every mathematician you meet ten you'd better give it the appropriate unit vector..
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Old Apr 24th 2018, 09:41 AM   #7
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Clarification of what woody and avito009 said.

Originally Posted by studiot View Post
There is no such thing as a one dimensional vector in Physics.
When I say a one dimensional vector I mean a vector on a one dimensional graph.



So you have only negative positive and zero here.
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Old Apr 24th 2018, 10:16 AM   #8
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There is a subtle feature of vectors, they are relative quantities.

So while a scalar quantity in 1D space defines a position on the number line
a vector quantity defines a change in position.
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Old Apr 24th 2018, 10:41 AM   #9
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Originally Posted by Woody View Post
There is a subtle feature of vectors, they are relative quantities.

So while a scalar quantity in 1D space defines a position on the number line
a vector quantity defines a change in position.
What position on which number line does 4 represent? Vectors don't always define changes. E.g. the position vector of a stationary particle doesn't.
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Old Apr 24th 2018, 10:43 AM   #10
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Originally Posted by avito009 View Post
When I say a one dimensional vector I mean a vector on a one dimensional graph.



So you have only negative positive and zero here.
You're trying awfully hard to make your ideas fit into a world in which they play no role. Why?
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