Can Vector Units Be Simplified or Must Each Element Carry Units?

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The discussion centers on whether vector units should be placed outside the vector notation or included with each element. Clarity is emphasized, with the preference for including units within the vector to avoid ambiguity. Notation differences are also explored, noting that parentheses are typically for expressions, angle brackets for vectors, and square brackets for intervals. References to standards from BIPM and ISO support the argument for including units with vector components. Ultimately, the consensus leans towards maintaining clarity by placing units inside the vector notation.
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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,
(A, B, C)=(ae^{j\phi_1}, be^{j\phi_2}, ce^{j\phi_3}) H
or
(A, B, C)=(ae^{j\phi_1} H, be^{j\phi_2} H, ce^{j\phi_3} H)
 
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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.
 
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?
 
sandy.bridge said:
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_mathematical_symbols

which may answer your questions.
 
NemoReally said:
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.
 
jedishrfu said:
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/documents/jcgm/JCGM_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. :smile:
 
NemoReally said:
International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
3rd edition

http://www.bipm.org/utils/common/documents/jcgm/JCGM_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. :smile:

Yup, that nails it. Good to know. Thanks.

Also they suggest using ; instead of ,
 
sandy.bridge said:
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?

jedishrfu said:
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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