How about this
furious[a_, b_] := Module[{a1, a2, a3, b1, b2, b3, c},
{a1, a2, a3} = Transpose[a, {2, 3, 4, 1}];
{b1, b2, b3} = Transpose[b, {2, 3, 4, 1}];
c = {-a3 b2 + a2 b3, a3 b1 - a1 b3, -a2 b1 + a1 b2};
Transpose[c, {4, 1, 2, 3}]]
Simon Woods
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