Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: vector components and notation



John Mallinkrodt wrote:


Joel Rauber wrote:

I rather like the use of the vectors A_x and A_y, as they
provide a nice
geometric approach to introducing the idea of components.
One has probably
just finished defining vector addition geometrically
(head-to-tail and
parallel transport). Its then natural to define component
vectors as those
unique vectors parallel to the coordinate axes that add up
to the vector A.

One can then write:

A_x vector = (A_x) i_hat etc

As John Denker mentioned, this may be just fine for us since we can
interpret what was *meant*. But students already have enough trouble
distinguishing between vectors, magnitudes of vectors (which are
nonnegative scalars), and components of vectors (which are signed
scalars.) They don't need us to make their lives even harder by
using inconsistent notation.

Agreed!!!

, I don't believe the above is inconsistant, barring typos and lack of
attention notational detail.


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: 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.)

<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>