help with proof

[jlmac2001]

How would I solve E1jk without the summation? I know how to solve it using the summation symbol but don't know howto do it without it.


Also, I need help proving that |torque|^2 = |r x F|^2= r^2F^2sin@(thetarF ). r dot F = rF cos (thetarF . Would I have to use (r x F) dot (r x F)?

[himanshu121]

The Qs are not clear to me
Does E represents Electric field

And What do u want to prove for Torque

[jlmac2001]

I need help with the third one in number 1 and numbers 2(proof) and 3. For number 3, how would I expand?

[himanshu121]

I still dont know what does epsilon delta represents may u have some notations

But as far as Q3 goes
The angle between \vec r x \vec F is zero
Hence (\vec r x \vec F).(\vec r x \vec F) = |(\vec r x \vec F)^2|

[HallsofIvy]

As himashu121 pointed out, in order to find ε1jk, you have to know what εijk means! I suspect I do know what it means since it is just a matter of looking up a definition, it would be much better for you to do that.

Right out the formula for εijk, and substitute i= 1- in fact, write out all the components and then just copy down those that have i=1.

[himanshu121]

I still want to know epsilon and delta i believe these are vector components

Though for Part2:

Write a=wx(wxr) = (w.r)w-(w.w)r where all are vectors and x is a cross product.

If r is perpendicular than w.r=0

[HallsofIvy]

Since jlmac2001 hasn't responded: In tensor analysis, δij is the tensor represented by the unit matrix: 1 if i=j, 0 otherwise.

εijk is the "alternating" tensor. It is defined to be: 1 if ijk is an even permutation of 123, -1 if ijk is an odd permutation of 123, 0 otherwise (i.e. if any one of the indices is repeated).

εsub]1jk[/sub] is therefore:
ε111= 0
ε112= 0
ε113= 0
ε121= 0
ε122= 0
ε123= 1
ε131= 0
ε132= -1
ε133= 0

Written as a matrix this would be:
[0 0 0]
[0 0 1]
[0 -1 0]