wolfe8
  • wolfe8
HALP! Question is in the picture. My problem is: I am not sure about j as in, will that have values 1 to 3 also? I think all I have to do is do all with i,j, and k having values 1,2 and 3. Can you give me one example for i=1, j=2 and k=3?
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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wolfe8
  • wolfe8
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anonymous
  • anonymous
what class is this from?
wolfe8
  • wolfe8
Theoretical mechanics. It's the vectors and scalars section in the beginning.

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anonymous
  • anonymous
what does \[\sum_{j}^{}\] represent?
wolfe8
  • wolfe8
Sum over j I think
anonymous
  • anonymous
it would seem to be the sum from J to something, but I'm not sure what... maybe the sum of all possible values of j?
wolfe8
  • wolfe8
Well yes. So I was wondering if I had to put in values from 1 to 3 for j as well. Which would mean a lot of work.
anonymous
  • anonymous
try it
anonymous
  • anonymous
and what is the significance of delta?
wolfe8
  • wolfe8
That's the Kronecker delta. Uh, if you don't know it, I'm not sure you know what I'm asking with my question...
anonymous
  • anonymous
I learn quickly, and who else is helping?
wolfe8
  • wolfe8
No one for now...
anonymous
  • anonymous
is this what it is? http://upload.wikimedia.org/math/3/7/f/37fd18cc5dc41b3ec1f6a26d7ff59c7a.png
wolfe8
  • wolfe8
Yup yup!
anonymous
  • anonymous
seems like you write out the result for 27 ordered triples
anonymous
  • anonymous
it won't take you an hour
wolfe8
  • wolfe8
Yeah I did exactly that and 3 of them violate the eqauation
anonymous
  • anonymous
which 3?
anonymous
  • anonymous
if you think about it, what it's saying is that if i=j and j=k, than i=k
anonymous
  • anonymous
so the three exceptions are when i=k but i isn't equal to j?
wolfe8
  • wolfe8
When i=k but not =j
anonymous
  • anonymous
These are Unit vectors (i,j&k) are perpendicular to each other. ixj=1x1 sin90 degree k=k, if we change order jxi= -k jxk=1x1 sin90 degree i=j, if we change the order kxj= -i kxi= 1x1 sin90 degree j=i, if we change the order ixk= =j
wolfe8
  • wolfe8
Yeah I had a feeling it has something to do with that. I missed that class because I was sick :/ I will have to re-learn it. Too bad I can't answer this question this time. Thanks for your help :)
anonymous
  • anonymous
@Ryaan "Don’t confuse the use of the dummy summation variables i, j, k, each of which can be 1, 2, or 3, with the unit vectors ˆi, ˆj, kˆ. These are two independent notations!" from http://physastro-msci.tripod.com/webonmediacontents/KroneckerDelta.pdf
wolfe8
  • wolfe8
I'm guessing it has something to do with this: http://www.physics.ohio-state.edu/~jay/555/tensor
anonymous
  • anonymous
Sorry! I don't know much..What I knew I've written!

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