Re: vector components and notation

[Bob LaMontagne <rlamont@POSTOFFICE.PROVIDENCE.EDU>]

One of the reasons that I have used Serway (Physics for Scientists and Engineers) is because I feel he is one of the few authors who really presents the concept of components correctly and also very clearly explains the concept to the student. The Vectors Ax and Ay that can add vectorially to form the vector A are _not_ the components. The true components are the _scalar_  projections of the the vector A onto the x and y axes. As scalars, they can be positive or negative depending on which side of the axes they project. Serway, to his
credit, carefully avoids assigning a sign to the vectors Ax and Ay. I will certainly take a good look at Hecht's 2003 text if it also takes a similarly clear and correct approach.  Hecht is extremely skilled in getting across the 'conceptual' aspect of physics.

Thanks - Bob at PC


Joe Heafner wrote:

> Fellow readers,
>
> In the preface to his new alg/trig based textbook (Physics: Algebra/Trig, 3rd edition. Brooks/Cole, 2003), Hecht finally begins to address the issue of contradictory notation used to explain vector components. Components are two orthogonal vectors that add to give a given original vector. Vectors don't have an algebraic sign about them; they are independent geometric entities with their own properties. Vector *components*, however may be treated as positive or negative with respect to a given coordinate axis. Herein lies the confusion.
>
> How can a vector *component* be both a vector and a scalar? I don't think that's possible. When we form the dot product of a vector with, say, an arbitrarily defined x-axis we get a *scalar*. How can we then justify calling this thing a vector? I don't think we can call it the magnitude of a vector either since magnitudes are always algebraically positive. Dot products can be positive or negative. I suspect the problem lies with the flawed usage of the term *component*.
>
> I am currently reading, for the second time, Gabriel Weinreich's excellent book Geometrical Vectors. If anyone would like to discuss certain aspects of this excellent little book on this list, I'd be grateful becuase I have some questions about some things.
>
> Cheers,
> Joe Heafner - Instructional Astronomy and Physics
> Home Page http://users.vnet.net/heafnerj/index.html
> I don't have a Lexus, but I do have a Mac. Same thing.