The proof of mass vector.
in [Math]
|
Prev: infinity ...
Next: The set of All sets
From: Eric Gisse on 26 Apr 2007 06:43 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.
From: Eric Gisse on 26 Apr 2007 06:43 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.
From: Eric Gisse on 26 Apr 2007 06:43 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.
From: briggs on 26 Apr 2007 09:06 In article <lPqXh.160$25.93(a)news.uchicago.edu>, mmeron(a)cars3.uchicago.edu writes: > In article <VE2FF$JAnAn+(a)eisner.encompasserve.org>, briggs(a)encompasserve.org writes: >>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, Note the parentheticals. I'm not talking about "scalar dot product". I'm talking about the product of a vector multiplied by a scalar. If you invert aB = C for scalar a, vector B and vector C to derive "C divided by B is a" then B and C had better be parallel Unless C is zero, of course.
From: mmeron on 26 Apr 2007 16:14
In article <6T7EHeFkCC01(a)eisner.encompasserve.org>, briggs(a)encompasserve.org writes: >In article <lPqXh.160$25.93(a)news.uchicago.edu>, mmeron(a)cars3.uchicago.edu writes: >> In article <VE2FF$JAnAn+(a)eisner.encompasserve.org>, briggs(a)encompasserve.org writes: >>>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, > >Note the parentheticals. I'm not talking about "scalar dot product". >I'm talking about the product of a vector multiplied by a scalar. Well, the reason I included the parentheticals is that there appeared to be a terminology confusion present. The term "scalar product" is used for a product of two vectors yielding scalar, it is synonymous with "dpt product" and "inner product" (and there is no such term as "scalar dot product", that's redundant). The product you refer to really has no special name, AFAIK. In any case, you're quite right regarding... > >If you invert aB = C for scalar a, vector B and vector C to >derive "C divided by B is a" then B and C had better be parallel > >Unless C is zero, of course. Thus, such operation is of little use, of course. Mati Meron | "When you argue with a fool, meron(a)cars.uchicago.edu | chances are he is doing just the same" |