dot product, cross product

dot product, cross product

Post by Russ Keple » Tue, 06 Feb 2001 07:40:35



All,

I'm hoping that someone has a good reference to help me get refreshed on
some beginning math for physics.  Dimensional analysis doesn't bother
me, but the vector math I just can't recall, and my son is wanting help
with his homework...  My last exposure was a bit over 25 years ago, and
it's just not clicking anymore.

A web reference would be most useful, but even a good book that gets
into this would be of help...

--

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dot product, cross product

Post by Ed Huntres » Tue, 06 Feb 2001 08:19:58


What grade is your son in?

The book that a lot of algebra teachers are recommending now to *parents*,
who want a great reference book to help their children with math, is
"Algebra To Go", by Great Source Education Group, a Houghton Mifflin
Company. Published 2000. I love it. So do other parents. It covers a lot of
geometry as well as algebra, and it's organized so you can use it as a
reference, without reading it cover-to-cover. I didn't think that would work
but it does.

As for websites, I haven't found one to beat "Dr. Math",
http://forum.swarthmore.edu/dr.math/.

Ed Huntress

 
 
 

dot product, cross product

Post by mulli.. » Tue, 06 Feb 2001 10:10:26




Quote:
> A web reference would be most useful, but even a good book that gets
> into this would be of help...

Back when I was a boy.... (dad, stop it!) I used "Calculus, One
and Several Variables" by Salas and Hill. Had a quite decent
section on vectors and things like dot and cross products.

Jim

Sent via Deja.com
http://www.deja.com/

 
 
 

dot product, cross product

Post by Mike Grah » Tue, 06 Feb 2001 11:56:07


Quote:

>A web reference would be most useful, but even a good book that gets
>into this would be of help...

  I distinctly remember first year algebra.  I don't remember the
professor's name, but I definately could still pick his voice out of a
crowd.  He was an east indian, and he had some classic vocal mannerisms.
  As we discussed 'wector spaces' and whatnot he'd often start off with
"First, select a point that you like veddyveddy much.  Then select a second
point that you like veddyveddy much, but not the same as the first point."
  I liked that guy.  8-)

  Anyway, the book was pretty decent, and it was called Elementary Linear
Algebra with Applications by Anton and Rorres.

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dot product, cross product

Post by Spehro Pefhan » Tue, 06 Feb 2001 12:17:40



Quote:
>   Anyway, the book was pretty decent, and it was called Elementary Linear
> Algebra with Applications by Anton and Rorres.

I still have my faded Schaum's Outline _Linear Algebra_ by Seymour
Lipschutz. "Including 600 Solved Problems". You can get it for $7 plus
$3 shipping used from Gail's books in Richland WA.  

Best regards,
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dot product, cross product

Post by Doug Gonc » Tue, 06 Feb 2001 17:17:51


The overview is that the dot product is a number, a scalar, while the cross
product is another vector, same as the two operated upon.

http://www.plmsc.psu.edu/~www/matsc597/vectors/

is one I found with google:

http://www.google.com/search?q=vectors%2C+matrices%2C+tensors

that way.

Retraction: "You may post this. I haven't." was for personal replies. Left it
in the sig.

Yours,

Doug

 
 
 

dot product, cross product

Post by Norman Yarv » Wed, 07 Feb 2001 02:36:36


Quote:

>I'm hoping that someone has a good reference to help me get refreshed on
>some beginning math for physics.  Dimensional analysis doesn't bother
>me, but the vector math I just can't recall, and my son is wanting help
>with his homework...  My last exposure was a bit over 25 years ago, and
>it's just not clicking anymore.

>A web reference would be most useful, but even a good book that gets
>into this would be of help...

The book "Div, grad, curl, and all that: an informal text on vector
calculus" is not bad.  (Which is about the highest praise I've ever been
able to give to a mathematics text.)  It even approaches being readable.
 
 
 

dot product, cross product

Post by Spehro Pefhan » Thu, 08 Feb 2001 21:59:31



Quote:
> And if you really enjoy this stuff (I do), dig up a copy of McConnell,
> "Applications of Tensor Analysis".  Dot and cross products become
> trivial straight forward items.  You even learn that the so-called cross
> product can only be represented by a vector in a three dimensional
> space.

That's how I think of it, a vector pointing out in 3-space from the point
where the two other two vectors are made to touch (tail to head). I can't
think of where I got that visualization, though (it was from a book). For
something like torque it is  very intuitive. The dot product I think of as
something like the length of the shadow (cos theta) of one vector on the
other (it's just a scalar, of course).

P.S. To be pedantic, the dot product is only a vector in 3-d space if the
other two vectors were in 2-d space to begin with, but the visualization
is still very useful.

Best regards,
--
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Spehro Pefhany --"it's the network..."            "The Journey is the reward"

Embedded software/hardware/analog  Info for designers:  http://www.speff.com
Contributions invited->The AVR-gcc FAQ is at: http://www.BlueCollarLinux.com
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dot product, cross product

Post by Ted Edward » Fri, 09 Feb 2001 01:59:12


Quote:

> That's how I think of it, a vector pointing out in 3-space from the point
> where the two other two vectors are made to touch (tail to head).

For cross product, think tail to tail with a third vector, tail to the
other tails and perpendicular to the plane of the first two.  Direction
by the right hand rule.  Magnitude A B Sin a where A and B are the
magnitudes of vectors A and B and a is the angle between them.  This
only works in 3 space.

Quote:
> P.S. To be pedantic, the dot product is only a vector in 3-d space if the
> other two vectors were in 2-d space to begin with, but the visualization
> is still very useful.

You must have meant cross product there.  The dot product is a scalar in
any dimension space.

Ted

 
 
 

dot product, cross product

Post by Spehro Pefhan » Fri, 09 Feb 2001 02:26:32



Quote:
> You must have meant cross product there.  The dot product is a scalar in
> any dimension space.

Yup. Thanks, and I see you had already mentioned the 3-d thing in another
post.

Best regards,  
--
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=
Spehro Pefhany --"it's the network..."            "The Journey is the reward"

Embedded software/hardware/analog  Info for designers:  http://www.speff.com
Contributions invited->The AVR-gcc FAQ is at: http://www.BlueCollarLinux.com
=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=

 
 
 

dot product, cross product

Post by Joshua H. Gordi » Sat, 10 Feb 2001 15:32:12


Hey, nobody is talking about the outer product...

Josh Gordis


Quote:

> > The overview is that the dot product is a number, a scalar, while the
cross
> > product is another vector, same as the two operated upon.

> Only in 3-D.  Doesn't work for any other dimension space.

> Ted