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Vector Quantities

  1. Dec 6, 2009 #1

    Char. Limit

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    Can someone tell, using the unit of a physical measurement, if the measurement is a vector? For example, without knowing about force, can one tell by the unit kg-m/s^2 that force is a vector?

    I'm trying to say, for example, thay since the m in kg-m/s^2 is a vector (for example), the whole thing is a vector... I probably sound dumb...
  2. jcsd
  3. Dec 6, 2009 #2
    Does the unit or system have a magnitude of some sort? Does it have a direction of some sort? If it meets both conditions, it's a vector.
  4. Dec 6, 2009 #3

    Char. Limit

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    Well... let's say I invented a new, unused unit... I'll say m^2/s. Could you tell, just by that unit, if the quantity is a vector?
  5. Dec 7, 2009 #4


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    No. The units have nothing to do with whether the quantity is a vector or scalar. I could perhaps invent a vector quantity with the units m^2/s and a scalar quantity with the same units. Or even several of each.

    Example: take the unit of length, the meter. There is a vector quantity, displacement, and a scalar quantity, distance, that are both measured in meters.

    Example 2: Current, measured in amperes, can be a scalar or vector depending on who you ask.

    Caveat: for some units, there don't happen to be any meaningful vector quantities associated with them. For example, off the top of my head I can't think of a vector quantity with units of mass. Or time. But there's no mathematical reason that one couldn't be created.
    Last edited: Dec 7, 2009
  6. Dec 7, 2009 #5

    Char. Limit

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  7. Dec 7, 2009 #6
    I am confusing myself a little. When you say "the velocity is 5 m/s north", you really are saying "the magnitude of the velocity vector is 5 m/s, and the direction is north"- so the actual unit is attributed to the magnitude, a scalar. The vector itself doesn't have a unit, but is composed of a set of scalar components, each with their units. From this perspective, only scalars can have units. I could feasibly construct a vector [x,y] in which x and y are scalars with different units, for example in polar coordinates x is a distance and y is dimensionless (the polar angle, in radians, so a ratio of two distances), then there is no convention I know of how to give this vector a unit.

    For me it is meaningless to say the vector has units... the vector gives you the location of a point in whatever space you are talking about, and a point does not have units. The distance in that space to a set of normal planes can have units, however, so each component can have units.

    Any disagreement with this view?
    Last edited: Dec 7, 2009
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