Question

Problem 3. In the following expressions, ? represents the Kronecker delta symbol, ? represents the Levi-Civita totally anti-symmetric tensor, P stands for the permutation operation, A and B are two vectors, and the Einstein Summation convention is assumed to be in effect. All indices run from 1 to 3. In each case below, carry out any implied summations over paired indices to evaluate the expression to a number, or, if that is not possible, reduce it to its simplest possible form. (Total 16 pts, 2 pts each) (a) ??? = (b) ??? = (c) ???? = (d) ??????? = (e) ?????????? = (f) P???(a, b, c) = (g) ????A?A? = (h) A?B???? =

          Problem 3. In the following expressions, ? represents the Kronecker delta symbol, ? represents the Levi-Civita totally anti-symmetric tensor, P stands for the permutation operation, A and B are two vectors, and the Einstein Summation convention is assumed to be in effect. All indices run from 1 to 3. In each case below, carry out any implied summations over paired indices to evaluate the expression to a number, or, if that is not possible, reduce it to its simplest possible form. (Total 16 pts, 2 pts each)

(a) ??? =
(b) ??? =
(c) ???? =
(d) ??????? =
(e) ?????????? =
(f) P???(a, b, c) =
(g) ????A?A? =
(h) A?B???? =

Problem 3. In the following expressions, ? represents the Kronecker delta symbol, ? represents the Levi-Civita totally anti-symmetric tensor, P stands for the permutation operation, A and B are two vectors, and the Einstein Summation convention is assumed to be in effect. All indices run from 1 to 3. In each case below, carry out any implied summations over paired indices to evaluate the expression to a number, or, if that is not possible, reduce it to its simplest possible form. (Total 16 pts, 2 pts each)

(a) ??? =
(b) ??? =
(c) ???? =
(d) ??????? =
(e) ?????????? =
(f) P???(a, b, c) =
(g) ????A?A? =
(h) A?B???? =

Added by Marco K.

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