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Quick question regarding vectors

by sandy.bridge
Tags: vectors
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sandy.bridge
#1
Feb6-13, 05:48 PM
P: 778
If I have a vector defining numerous quantities of the same units, can I merely place the units outside of the vector, or is it required to have units on every entity within the vector?

For example,
[tex](A, B, C)=(ae^{j\phi_1}, be^{j\phi_2}, ce^{j\phi_3}) H[/tex]
or
[tex](A, B, C)=(ae^{j\phi_1} H, be^{j\phi_2} H, ce^{j\phi_3} H)[/tex]
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jedishrfu
#2
Feb6-13, 05:53 PM
P: 3,001
My two cents is for clarity place the units of measure inside. Its not a factor.

For example, a position vector r=<1.0m,2.0m,3.0m> is much clearer than <1.0,2.0,3.0> m as someone might think its some undefined constant.
sandy.bridge
#3
Feb6-13, 05:57 PM
P: 778
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?

jedishrfu
#4
Feb6-13, 06:21 PM
P: 3,001
Quick question regarding vectors

Quote Quote by sandy.bridge View Post
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?
I can't answer for mathematicians but ( ) are usually for expressions, <> for vectors and [ ] intervals.

But I did find this:

http://en.wikipedia.org/wiki/List_of...atical_symbols

which may answer your questions.
NemoReally
#5
Feb6-13, 06:34 PM
P: 194
You can place the unit outside of the delimiter - see, for example, http://physics.nist.gov/Pubs/SP811/sec07.html section 7.7 (I believe the SP811 follows the ISO 31000 series in this respect)
jedishrfu
#6
Feb6-13, 09:20 PM
P: 3,001
Quote Quote by NemoReally View Post
You can place the unit outside of the delimiter - see, for example, http://physics.nist.gov/Pubs/SP811/sec07.html section 7.7 (I believe the SP811 follows the ISO 31000 series in this respect)
Nice article, I would still question this for a vector although I did see a list of values in parens with the uom at the end as the preferred list method.
NemoReally
#7
Feb7-13, 01:15 PM
P: 194
Quote Quote by jedishrfu View Post
Nice article, I would still question this for a vector although I did see a list of values in parens with the uom at the end as the preferred list method.
International vocabulary of metrology Basic and general concepts and associated terms (VIM)
3rd edition

http://www.bipm.org/utils/common/doc...M_200_2012.pdf

1 Quantities and units
1.1 (1.1)
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference
NOTE 5 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities, is also considered to be a quantity.

1.19 (1.18)
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
NOTE 4 In the case of vector or tensor quantities, each component has a quantity value.
EXAMPLE Force acting on a given particle, e.g. in Cartesian components (Fx; Fy; Fz) = (-31.5; 43.2; 17.0) N.

... if it's good enough for the BIPM and ISO, it's good enough for me.
jedishrfu
#8
Feb7-13, 02:55 PM
P: 3,001
Quote Quote by NemoReally View Post
International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
3rd edition

http://www.bipm.org/utils/common/doc...M_200_2012.pdf

1 Quantities and units
1.1 (1.1)
quantity
property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed as a number and a reference
NOTE 5 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities, is also considered to be a quantity.

1.19 (1.18)
quantity value
value of a quantity
value
number and reference together expressing magnitude of a quantity
NOTE 4 In the case of vector or tensor quantities, each component has a quantity value.
EXAMPLE Force acting on a given particle, e.g. in Cartesian components (Fx; Fy; Fz) = (-31.5; 43.2; 17.0) N.

... if it's good enough for the BIPM and ISO, it's good enough for me.
Yup, that nails it. Good to know. Thanks.

Also they suggest using ; instead of ,
HallsofIvy
#9
Feb7-13, 03:07 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,565
Quote Quote by sandy.bridge View Post
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?
Quote Quote by jedishrfu View Post
I can't answer for mathematicians but ( ) are usually for expressions, <> for vectors and [ ] intervals.
Speaking for mathematicians, the real problem is that points are represented, in a Cartesian coordinate system, as (x, y, z), writing vectors as <a, b, c> is less confusing that using (a, b, c).


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