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-----Original Message-----
From: Bob LaMontagne [mailto:rlamont@POSTOFFICE.PROVIDENCE.EDU]
Sent: Monday, September 16, 2002 5:14 PM
To: PHYS-L@lists.nau.edu
Subject: Re: vector components and notation
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,Algebra/Trig, 3rd edition. Brooks/Cole, 2003), Hecht finally
In the preface to his new alg/trig based textbook (Physics:
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.
I don't think that's possible. When we form the dot product
How can a vector *component* be both a vector and a scalar?
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*.
Weinreich's excellent book Geometrical Vectors. If anyone
I am currently reading, for the second time, Gabriel
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.