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Teachers' Lounge Discussion: Vector orientation

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From: Loyd <loydlin@aol.com>
To: Teacher2Teacher Public Discussion
Date: 2007021814:32:34
Subject: Re: Vectors - dot.product and cross product

On 2001062117:39:50, John Oke wrote:
>I have a lot of difficulty in understanding the meaning and
>computation of dot.products and cross products. My other problem is
>being able to state the angle between a line and a plane. Is it
>possible to explain these in easy terms/words for an average student.
>I shall be verygrateful	
>

There is a wealth of information on dot and cross product on the web. 
I too, have always wanted a better understanding of these two vector
operations.  Go to Google and search for "Cross Product."  Lots of
information. 

I have a TI-89 and this calculator has cross product built in and it
also has dot product (I have to use magnifying glass to see TI-89
screen).  In fact just the other day, I happened to look at a Cliff
Notes book for linear algebra and saw cross product explained and that
brought back college days memories when I was first exposed to what I
though was very abstract.   I happened to look in my TI-89 book and
saw that it could do cross product.  

Then a few days later, I talked to a pre med student at a major
university who was also having some difficulty with cross product.  I
mentioned that the TI-89 could do this operation.  The student was
surprised because they used that model in class.  

After reading your post, I looked on Google and searched for cross
product with TI -89 and came up with this at:

http://www.tcc.edu/faculty/webpages/PGordy/Egr140/CrossDot.pdf


"Determining cross products and dot products by hand:
P x Q = (1i + 2j + 3k) x (5i + 0j - 1k)
= 5(i x i) + 0(i x j) - 1(i x k) +10(j x i) + 0(j x j) - 2(j x k) +
15(k x i) + 0(k x j) - 3(k x k)
= 5(0) + 0(k) - 1(-j) + 10(-k) + 0(0) - 2(i) + 15(j) + 0(-i) - 3(0)
= -2i + 16j - 10k
= (-2,16,-10)
P  Q = (1i + 2j + 3k)  (5i + 0j - 1k) = (1)(5) + (2)(0) + (3)(-1) =
5 + 0 - 3 = 2"

That is the first time that I have seen this hand method.  The pattern
is easy to follow.  On the TI 89, I went to Math, Vector ops, cross
product and did this:

crossP( [ 1, 2, 3 ] , [ 5, 0, -1 ] ) enter and the answer comes up.

The above PDF paper says use catalog.  I didn't try that.  One web
site said use the TI-89 for homework if need be, but it was not
allowed on exams.  Too easy! 

The cross product has application in electicity and magnetisim.  In
the early days electricity and magnetisim were separate fields and
Oersted discovered in a class that if a compass is parrallel to a wire
with current flow,  the needle would swing to a right angle position. 
Thus, electricity and magnetisim were related.  I have also seen cross
product used in mechanics courses.  

 



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