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Quick question regarding vectors

  1. Feb 6, 2013 #1
    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]
    [tex](A, B, C)=(ae^{j\phi_1} H, be^{j\phi_2} H, ce^{j\phi_3} H)[/tex]
  2. jcsd
  3. Feb 6, 2013 #2


    Staff: Mentor

    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.
  4. Feb 6, 2013 #3
    Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?
  5. Feb 6, 2013 #4


    Staff: Mentor

    I can't answer for mathematicians but ( ) are usually for expressions, <> for vectors and [ ] intervals.

    But I did find this:


    which may answer your questions.
  6. Feb 6, 2013 #5
    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)
  7. Feb 6, 2013 #6


    Staff: Mentor

    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.
  8. Feb 7, 2013 #7
    International vocabulary of metrology – Basic and general concepts and associated terms (VIM)
    3rd edition


    1 Quantities and units
    1.1 (1.1)
    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
    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:
  9. Feb 7, 2013 #8


    Staff: Mentor

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

    Also they suggest using ; instead of ,
  10. Feb 7, 2013 #9


    User Avatar
    Science Advisor

    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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