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“Vector quantity” --More than two dimensions?

How, in simplest possible terms, does one determine the speed an object is traveling along a given vector?“Similarity” of two vectorsWhy Force is called a vector quantity?If vectors are represented as a set of points like a coordinate, how can they be translated/moved?Pythagorean theorem in higher dimensions?Concept: Multiplying a vector by a scalar quantityFinding vector length for high dimensionsCross product in 4 dimensionsFinding a vector in 3 dimensionsVector product in two dimensions

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2

1

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Is the term "vector" used exclusively to refer to quantities of two dimensions, or can it also refer to quantities of more than two dimensions, for instance, magnitude, direction, and weight?

vectors terminology definition

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edited 8 hours ago

Jack

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asked 9 hours ago

Jim SimsonJim Simson

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Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Did you take a linear algebra or vector calculus class?
  $endgroup$
  – Moishe Kohan
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Decades ago my friend.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  en.wikipedia.org/wiki/Vector_(mathematics_and_physics)
  $endgroup$
  – Jack
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Jack, I certainly checked there before posting, however, at least for me (someone with an untrained mathematical mind) it did not seem to clearly answer my question.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  

add a comment | 

2

1

$begingroup$

Is the term "vector" used exclusively to refer to quantities of two dimensions, or can it also refer to quantities of more than two dimensions, for instance, magnitude, direction, and weight?

vectors terminology definition

share|cite|improve this question

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

asked 9 hours ago

Jim SimsonJim Simson

11344 bronze badges

New contributor

Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Did you take a linear algebra or vector calculus class?
  $endgroup$
  – Moishe Kohan
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Decades ago my friend.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  en.wikipedia.org/wiki/Vector_(mathematics_and_physics)
  $endgroup$
  – Jack
  9 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Jack, I certainly checked there before posting, however, at least for me (someone with an untrained mathematical mind) it did not seem to clearly answer my question.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Is the term "vector" used exclusively to refer to quantities of two dimensions, or can it also refer to quantities of more than two dimensions, for instance, magnitude, direction, and weight?

vectors terminology definition

share|cite|improve this question

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

asked 9 hours ago

Jim SimsonJim Simson

11344 bronze badges

New contributor

Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

$endgroup$

share|cite|improve this question

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

asked 9 hours ago

Jim SimsonJim Simson

11344 bronze badges

New contributor

Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

share|cite|improve this question

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

asked 9 hours ago

Jim SimsonJim Simson

11344 bronze badges

New contributor

Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

edited 8 hours ago

Jack

28.3k1818 gold badges8484 silver badges210210 bronze badges

asked 9 hours ago

Jim SimsonJim Simson

11344 bronze badges

New contributor

Jim Simson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.

asked 9 hours ago

Jim SimsonJim Simson

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2 Answers
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11

$begingroup$

Mathematicians don't like to categorically say what the basic things of study are. It has turned out to be much more fruitful to say how things behave, and then every time we come across something which behaves that way, we can apply all the theory we already developed to that thing.

Vectors is one of those concepts that we have defined in terms of behaviour rather than content, and that behaviour is summed up in a few neat axioms. Those axioms basically says that for a collection of "things" to deserve the name vector space (and thus for each "thing" to be deemed a vector):

You can add things from your collection together to make a new thing (and this thing has to be in your collection already). You can scale a thing to make a new thing (and this new thing has to already be in your collection). This adding and scaling work together through distribution (the way regular addition and multiplication work together through distribution).

The actual list is a whole lot more formal, and I glossed over a few requirements, but this is the gist of it. If your collection follows the demands, then it gets to call itself a vector space, and the things become vectors.

So any time you have a collection of things that have this particular vector-space-behaviour, then what you have is a vector space and each thing in that collection is a vector. Dimension is not a part of what we require of a vector space. In particular, a dimension of 2 is not something we require; plenty of commonly used vector spaces (even some in use in middle and high school, without the students realizing it) even have an infinite number of dimensions.

share|cite|improve this answer

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Arthur, that helps immensely. Thank you.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  

add a comment | 

1

$begingroup$

The term vector can have any number of positive integer dimensions. The important thing is that it has both a magnitude and a direction.

share|cite|improve this answer

answered 9 hours ago

DMcMorDMcMor

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add a comment | 

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11

$begingroup$

Mathematicians don't like to categorically say what the basic things of study are. It has turned out to be much more fruitful to say how things behave, and then every time we come across something which behaves that way, we can apply all the theory we already developed to that thing.

Vectors is one of those concepts that we have defined in terms of behaviour rather than content, and that behaviour is summed up in a few neat axioms. Those axioms basically says that for a collection of "things" to deserve the name vector space (and thus for each "thing" to be deemed a vector):

You can add things from your collection together to make a new thing (and this thing has to be in your collection already). You can scale a thing to make a new thing (and this new thing has to already be in your collection). This adding and scaling work together through distribution (the way regular addition and multiplication work together through distribution).

The actual list is a whole lot more formal, and I glossed over a few requirements, but this is the gist of it. If your collection follows the demands, then it gets to call itself a vector space, and the things become vectors.

So any time you have a collection of things that have this particular vector-space-behaviour, then what you have is a vector space and each thing in that collection is a vector. Dimension is not a part of what we require of a vector space. In particular, a dimension of 2 is not something we require; plenty of commonly used vector spaces (even some in use in middle and high school, without the students realizing it) even have an infinite number of dimensions.

share|cite|improve this answer

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Arthur, that helps immensely. Thank you.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  

add a comment | 

11

$begingroup$

Mathematicians don't like to categorically say what the basic things of study are. It has turned out to be much more fruitful to say how things behave, and then every time we come across something which behaves that way, we can apply all the theory we already developed to that thing.

Vectors is one of those concepts that we have defined in terms of behaviour rather than content, and that behaviour is summed up in a few neat axioms. Those axioms basically says that for a collection of "things" to deserve the name vector space (and thus for each "thing" to be deemed a vector):

You can add things from your collection together to make a new thing (and this thing has to be in your collection already). You can scale a thing to make a new thing (and this new thing has to already be in your collection). This adding and scaling work together through distribution (the way regular addition and multiplication work together through distribution).

The actual list is a whole lot more formal, and I glossed over a few requirements, but this is the gist of it. If your collection follows the demands, then it gets to call itself a vector space, and the things become vectors.

So any time you have a collection of things that have this particular vector-space-behaviour, then what you have is a vector space and each thing in that collection is a vector. Dimension is not a part of what we require of a vector space. In particular, a dimension of 2 is not something we require; plenty of commonly used vector spaces (even some in use in middle and high school, without the students realizing it) even have an infinite number of dimensions.

share|cite|improve this answer

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Arthur, that helps immensely. Thank you.
  $endgroup$
  – Jim Simson
  9 hours ago
  

  
  
  
  

add a comment | 

$begingroup$

Mathematicians don't like to categorically say what the basic things of study are. It has turned out to be much more fruitful to say how things behave, and then every time we come across something which behaves that way, we can apply all the theory we already developed to that thing.

Vectors is one of those concepts that we have defined in terms of behaviour rather than content, and that behaviour is summed up in a few neat axioms. Those axioms basically says that for a collection of "things" to deserve the name vector space (and thus for each "thing" to be deemed a vector):

You can add things from your collection together to make a new thing (and this thing has to be in your collection already). You can scale a thing to make a new thing (and this new thing has to already be in your collection). This adding and scaling work together through distribution (the way regular addition and multiplication work together through distribution).

The actual list is a whole lot more formal, and I glossed over a few requirements, but this is the gist of it. If your collection follows the demands, then it gets to call itself a vector space, and the things become vectors.

So any time you have a collection of things that have this particular vector-space-behaviour, then what you have is a vector space and each thing in that collection is a vector. Dimension is not a part of what we require of a vector space. In particular, a dimension of 2 is not something we require; plenty of commonly used vector spaces (even some in use in middle and high school, without the students realizing it) even have an infinite number of dimensions.

share|cite|improve this answer

answered 9 hours ago

ArthurArthur

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$endgroup$

share|cite|improve this answer

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

answered 9 hours ago

ArthurArthur

130k88 gold badges126126 silver badges217217 bronze badges

1

$begingroup$

The term vector can have any number of positive integer dimensions. The important thing is that it has both a magnitude and a direction.

share|cite|improve this answer

answered 9 hours ago

DMcMorDMcMor

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$endgroup$

add a comment | 

1

$begingroup$

The term vector can have any number of positive integer dimensions. The important thing is that it has both a magnitude and a direction.

share|cite|improve this answer

answered 9 hours ago

DMcMorDMcMor

3,22533 gold badges1515 silver badges3131 bronze badges

$endgroup$

add a comment | 

$begingroup$

The term vector can have any number of positive integer dimensions. The important thing is that it has both a magnitude and a direction.

share|cite|improve this answer

answered 9 hours ago

DMcMorDMcMor

3,22533 gold badges1515 silver badges3131 bronze badges

$endgroup$

share|cite|improve this answer

answered 9 hours ago

DMcMorDMcMor

3,22533 gold badges1515 silver badges3131 bronze badges

answered 9 hours ago

DMcMorDMcMor

3,22533 gold badges1515 silver badges3131 bronze badges

answered 9 hours ago

DMcMorDMcMor

3,22533 gold badges1515 silver badges3131 bronze badges