Teacher2Teacher |
Q&A #6308 |
From: Loyd
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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