Quick question regarding vectors

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In summary, when dealing with vectors and quantities, it is recommended to place the units of measurement outside of the delimiter, such as in <1.0, 2.0, 3.0> m. This is to avoid confusion and clearly indicate the units. Additionally, the International vocabulary of metrology – Basic and general concepts and associated terms (VIM) suggests using ; instead of , for vectors. While mathematicians may use ( ) for expressions and <> for vectors, it is recommended to use < > for vectors to avoid confusion with points represented in a Cartesian coordinate system. Ultimately, the preferred notation may vary, but it is important to clearly indicate the units of measurement to avoid confusion.
  • #1
sandy.bridge
798
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]
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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  • #2
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.
 
  • #3
Perfect. Since we are on the topic: in regards to notation, is there a difference between using (, [, or <?
 
  • #5
  • #6
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.
 
  • #7
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:
 
  • #8
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 ,
 
  • #9
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).
 

What is a vector?

A vector is a mathematical quantity that has both magnitude (size) and direction. It is often represented by an arrow, with the length of the arrow indicating the magnitude and the direction of the arrow indicating the direction.

What are some examples of vectors?

Some examples of vectors include displacement, velocity, force, and acceleration. These quantities have both magnitude and direction, making them vectors.

How are vectors represented mathematically?

Vectors are typically represented as ordered sets of numbers, called components, in a coordinate system. For example, a two-dimensional vector can be represented as (x, y), where x and y are the components in the x and y directions, respectively.

What is the difference between a scalar and a vector?

A scalar is a quantity that only has magnitude, while a vector has both magnitude and direction. Examples of scalars include temperature, mass, and time, while examples of vectors include displacement, velocity, and force.

How are vectors used in science and engineering?

Vectors are used in many areas of science and engineering, including physics, mechanics, and computer graphics. They are used to represent and analyze physical quantities such as motion, forces, and electromagnetic fields, and they are essential for solving problems in these fields.

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