The proof of mass vector.
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From: Jeckyl on 24 Apr 2007 02:34 "Eric Gisse" <jowr.pi(a)gmail.com> wrote in message news:1177392764.172918.33290(a)b40g2000prd.googlegroups.com... > On Apr 23, 7:43 pm, "Jeckyl" <n...(a)nowhere.com> wrote: >> "Sam Wormley" <sworml...(a)mchsi.com> wrote in message >> >> news:BweXh.12286$n_.8438(a)attbi_s21... >> >> >> >> > Ka-In Yen wrote: >> >> On Apr 23, 9:41 pm, Bob Kolker <nowh...(a)nowhere.com> wrote: >> >>> Ka-In Yen wrote: >> >> >>>> Vector division can help we to calculate the components >> >>>> of vector. For example, we put a brick on a sloping surface. >> >>>> The mass of the brick is M, and the contacting area between >> >>>> the brick and the sloping surface is A. Then we have >> >>>> F=Mg (where g is the acceleration due to gravity.) >> >>>> pressure p= F/A = |F|cos(theta)/|A| >> >>> Which is a scalar, not a vector. >> >> >> Dear Bob Kolker, >> >> >> Thank you for your comment. Pressure(p) is a scalar. >> >> Force and area are vectors. >> >> > As I have shown you before, Ka-In Yen, area is not a vector quantity. >> >> Not that I've been following the thread, but maybe what is being referred >> to >> is the normal vector for the planar surface? > > He uses it as supporting evidence that area is a vector, despite not > being any kind of support for his argument in any way. > > Follow the thread in Google - it goes back to November of 2005. He > uses the same idiotic arguments, same pidgin notation that nobody but > him can understand, and arrives at the same idiotic conclusion. I noticed it went back a long way .. I don't really have the time or interest to follow it that far :)
From: briggs on 24 Apr 2007 09:56 In article <5954f6F2iv9rcU1(a)mid.individual.net>, Bob Kolker <nowhere(a)nowhere.com> writes: > Ka-In Yen wrote: >> >> Hamilton had discovered vector division in 1843. > > Which product are you using. The cross product (in which case there is > no division) or the dot product (in which case there is no division). Cross product does give rise to a division operation. It allows one to divide a vector by a vector yielding a vector. Alas, it is not very general. It requires that dividend and divisor be orthogonal and needs some way to prescribe the direction of the quotient. Dot product does give rise to a division operation. It allows one to divide a scalar by a vector yielding a vector. Alas, it needs some way to prescribe the direction of the quotient. Scalar product (multiplication of a scalar and a vector) gives rise to two division operations. Division of a vector by a scalar yielding a vector. Which is surely not controversial. And division of a vector by a vector yielding a scalar. Alas, this last operation is not very general since it requires that dividend and divisor be parallel. Of these operations, only two permit division of a vector by a vector. One yields a vector quotient and requires orthogonal inputs. One yields a scalar quotient and requires parallel inputs.
From: mmeron on 24 Apr 2007 13:07 In article <VE2FF$JAnAn+(a)eisner.encompasserve.org>, briggs(a)encompasserve.org writes: >In article <5954f6F2iv9rcU1(a)mid.individual.net>, Bob Kolker <nowhere(a)nowhere.com> writes: >> Ka-In Yen wrote: >>> >>> Hamilton had discovered vector division in 1843. >> >> Which product are you using. The cross product (in which case there is >> no division) or the dot product (in which case there is no division). > >Cross product does give rise to a division operation. It allows one >to divide a vector by a vector yielding a vector. Alas, it >is not very general. It requires that dividend and divisor be >orthogonal and needs some way to prescribe the direction of the >quotient. > >Dot product does give rise to a division operation. It allows one >to divide a scalar by a vector yielding a vector. Alas, it needs >some way to prescribe the direction of the quotient. > >Scalar product (multiplication of a scalar and a vector) gives rise >to two division operations. Division of a vector by a scalar yielding >a vector. Which is surely not controversial. And division of a >vector by a vector yielding a scalar. Alas, this last operation is >not very general since it requires that dividend and divisor be >parallel. > No, it doesn't, it is just that it isn't unique. You can define a multiplicative inverse (for dot product) of a vector v by the usual rule, i.e. the multiplicative inverse of v is a vector v^(-1) such that v /dot v' = 1. And it is easy to check that the vector v^(-1) = v/|v|^2 fits the bill. And once you defined the inverse this way, division naturally follows as u/v = u /dot v^(-1) = (u /dot v)/|v^2|. There is no requirement for u to be parallel to v here (though of course only the component of u parallel to v contributes to the result). The problem is that the multiplicative inverse defined this way is not unique since one can add to it an arbitrary vector orthogonal to v and the result V /dot v^(-1) = 1 will still hold (but the results for an arbitrary division will change). So, it has to be used with care. Note that uniqueness can be forced by adding an additional constraint, for example "the multiplicative inverse of v is the *shortest* of all vectors w satisfying v /dot w = 1." Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same"
From: Ka-In Yen on 25 Apr 2007 20:17 On Apr 24, 9:25 am, Bob Kolker <nowh...(a)nowhere.com> wrote: > Ka-In Yen wrote: > > > Dear Bob Kolker, > > > Thank you for your comment. Pressure(p) is a scalar. > > Force and area are vectors. > > Force can be represented by a vector. That is because forces have both > megnitude and direction. Area cannot. Area is a measure. What is the > direction of an area? Let's check this equation Pressure = Force / Area. If force is a vector and area is a scalar, then pressure is a vector. This is a disaster of physical mathematics.
From: Eric Gisse on 26 Apr 2007 06:01
On Apr 25, 4:17 pm, Ka-In Yen <yenk...(a)yahoo.com.tw> wrote: > On Apr 24, 9:25 am, Bob Kolker <nowh...(a)nowhere.com> wrote: > > > Ka-In Yen wrote: > > > > Dear Bob Kolker, > > > > Thank you for your comment. Pressure(p) is a scalar. > > > Force and area are vectors. > > > Force can be represented by a vector. That is because forces have both > > megnitude and direction. Area cannot. Area is a measure. What is the > > direction of an area? > > Let's check this equation Pressure = Force / Area. > If force is a vector and area is a scalar, then > pressure is a vector. This is a disaster of physical > mathematics. The only disaster is your freshman-level physics understanding. Quit trying to pull vectorial information from equations that are only valid in one dimension. |