Recently, Jose posted:
[...]
A vector has magnitude and direction. AOA has no direction in and of
itself.

[...]
What is the angle of attack? To be a scalar, it would have just
magnitude (which could include an algebraic sign). To be a vector, it
would have to have magnitude AND direction.

However, it is valid for a vector to have a magnitude of zero. It is NOT
valid for a scalar to have a directional component, and it is meaningless
to have an AOA with no directional component and magnitude (e.g. parked
aircraft have no AOA). Ergo, to have an AOA, you *must* also have velocity
(magnitude) and direction.

[...]
In this case, the angle of attack is twenty-one degrees. It is the
difference between the two angles given (with reference to the same
fuselage).

The two aspects of the AOA is referenced to the wing chord and relative
wind, not the fuselage.

There is no "direction" to this angle (except perhaps an
algebraic sign). So it is not a vector.

I'd say that it is often "OK" to PRESUME the directional components and
IGNORE their value if they are unimportant to usages where only the angle
is needed. But, that's quite a different situation than calling AOA
something it can't be by definition.

[...]
So, depending on context, angles can be magnitudes =or= directions,
but not both at once.

We're not talking about generic "angles", but an "Angle Of Attack", i.e.,
a specific usage which is defined by and inseparable from the components
of motion (aka relative wind). Without those components, AOA doesn't
exist.

Neil