Teacher2Teacher |
Q&A #6308 |
From: redwan
To: Teacher2Teacher Public Discussion
Date: 2007032504:51:20
Subject: Re: Re: Vectors - dot.product and cross product
On 2007021814:32:34, Loyd wrote: >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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