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June 26th, 2017, 08:43 PM   #1
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What is line vector?

I am reading a book on vector analysis, but the statement defining "line vector" confuses me because I can't catch the author's English, especially "forms a part". Following is a screenshot of this definition of line vector in the text, highlighted by a red line. Could you please tell me what a line vector is according to the text? Thanks a lot.


Last edited by skipjack; June 27th, 2017 at 12:44 AM.
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June 26th, 2017, 09:44 PM   #2
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The term is "line vector", not "linear vector".
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June 27th, 2017, 12:31 AM   #3
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I can't find "Edit", you are a moderator, can you edit it?
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June 27th, 2017, 12:46 AM   #4
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Done.
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June 28th, 2017, 08:20 AM   #5
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This is more the physics idea of a vector than the mathematics definition. (It has nothing to do with "Linear Algebra".)

The usual definition of "vector" allows that it be anywhere in space. The velocity vector of a bird can be anywhere the bird is. (That is sometimes called a "free" vector but even without "free" that is what is assumed.) A "bound" vector has its tail and head at specific points. A "line" vector is one that can be at any point on a given line in the direction of the vector.

Last edited by skipjack; June 28th, 2017 at 08:35 AM.
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June 28th, 2017, 11:21 AM   #6
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Which forum do you think it should be in instead of linear algebra? Algebra, abstract algebra, geometry?
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June 28th, 2017, 01:46 PM   #7
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Math Focus: Elementary mathematics and beyond
Physics, perhaps.
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June 28th, 2017, 11:27 PM   #8
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I suppose you can think of a line vector as a vector in 1-dimension. The "x-axis" we're all familiar with in a Cartesian coordinate system can be thought of as a Defined line vector where y=0 for all x....positive or negative.
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June 28th, 2017, 11:51 PM   #9
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Quote:
Originally Posted by Country Boy View Post
... A "line" vector is one that can be at any point on a given line in the direction of the vector.
So, do you mean the initial point should be on the given line, or the end point should be on the given line, or both?
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June 29th, 2017, 01:29 PM   #10
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Both.
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