Re: vector components and notation

[John Mallinckrodt <ajm@CSUPOMONA.EDU>]

Joel Rauber wrote:

>  John Mallinkrodt wrote:
>
>  > If there is a vector indicated by <bold>A</bold>_sub_x, then
>  > <italic>A</italic>_sub_x should formally represent the *magnitude* of
>  > that vector and, thus, would never have a negative value as it could
>  > if it instead represented the scalar x-component of the vector
>  > <bold>A</bold>.
>
> I'm not sure I follow:

Agreed.  See below.

> let me restate and clarify the notation that I
> believe is consistant
>
> (Small note: I'm a proponent of arrows over letters for vector quantities
> instead of boldfacing.  But I'll follow what you have done above for ASCII
> clarity.)

Ditto

> <bold>A</bold>   =   a vector
>
> <bold>A_x</bold>  = a component vector, John D's projection onto
> <bold>i_hat</bold>
>
> A_x = a scalar component = <bold>A</bold> dot <bold>i_hat</bold>
>
> |A_x| = a positive scalar, the length of the component vector
> <bold>A_x</bold>

It does appear that I am still failing to make my point.  I'll try once more:

By convention we write

  |<bold>A</bold>| = magnitude of the vector <bold>A</bold>

but we generally allow ourselves the notational shortcut

  A = |<bold>A</bold>|

In other words, when a textbook writes a quantity in bold face, it is
understood to be a vector and when that *same quantity* is written in
regular (but usually italicized) face, it is understood to represent
the *magnitude* of the vector which is always *nonnegative* quantity.
Thus, if we allow ourselves to refer to the vector

  <bold>A_x</bold>

then, logically, the quantity

  |<bold>A_x</bold>| = A_x

represents the *magnitude* of *that* vector and shouldn't *also* be
used to represent the scalar x_component of the (different) vector

  <bold>A</bold>

To avoid this ambiguity, I simply prefer never to use the notation

  <bold>A_x</bold>

John
--
   A. John Mallinckrodt        http://www.csupomona.edu/~ajm
   Professor of Physics      mailto:ajm@csupomona.edu
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