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Is it true that an infinitesimal area is a vector quantity and large area is a scalar quantity ?

Yashwanth S Prabhu
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  • small area? large area? – Kyle Kanos Aug 07 '19 at 13:00
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    small area means dA and large area you can say a plane sheet of paper. – Yashwanth S Prabhu Aug 07 '19 at 13:01
  • Hello. I have found useful information here https://www.quora.com/Is-area-a-scalar-or-vector-quantity –  Aug 07 '19 at 13:12
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    it is us who decide, sometimes, to use it either way. in calculating flux, for example, we'll associate to the infinitesimal areas a vector $d\vec{A}$ whose magnitude is, well, the infinitesimal area. in other occasions, we don't need that. it's just about convenience. imagine a sheet of dimensions $5\times6$ in $cm$, its area would be $30cm^2$, what do you think is keeping me from naming a vector $\vec{A}$ such that its magnitude is $30$ and associate it to the area in some way? – GDGDJKJ Aug 07 '19 at 13:15
  • I think we can always associate a "vector" with an infinitesimal area element that does transform like a vector under coordinate transformations. Such could be done for finite areas(which can be interpreted as just an integral over the infinitesimal area element). However the resultant "vector" that we expect to get from the integral may not be so trivial. For example, in curved space, we in general can't do an integral over a vector field and hence I think taking a finite area as a vector is not well defined. But, in case of flat space that can be done. – quirkyquark Aug 07 '19 at 13:20
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    essentially a dupe of https://physics.stackexchange.com/q/14165/25301 – Kyle Kanos Aug 07 '19 at 13:33

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