Question

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?

Answer 1

what class is this from?

Answer 2

Theoretical mechanics. It's the vectors and scalars section in the beginning.

Answer 3

what does \[\sum_{j}^{}\]
represent?

Answer 4

Sum over j I think

Answer 5

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?

Answer 6

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.

Answer 7

try it

Answer 8

and what is the significance of delta?

Answer 9

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...

Answer 10

I learn quickly, and who else is helping?

Answer 11

No one for now...

Answer 12

is this what it is? http://upload.wikimedia.org/math/3/7/f/37fd18cc5dc41b3ec1f6a26d7ff59c7a.png

Answer 13

Yup yup!

Answer 14

seems like you write out the result for 27 ordered triples

Answer 15

it won't take you an hour

Answer 16

Yeah I did exactly that and 3 of them violate the eqauation

Answer 17

which 3?

Answer 18

if you think about it, what it's saying is that if i=j and j=k, than i=k

Answer 19

so the three exceptions are when i=k but i isn't equal to j?

Answer 20

When i=k but not =j

Answer 21

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

Answer 22

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 :)

Answer 23

@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

Answer 24

I'm guessing it has something to do with this: http://www.physics.ohio-state.edu/~jay/555/tensor

Answer 25

Sorry! I don't know much..What I knew I've written!