(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If a, b, and c are any three vector fields in locally Minkowskain 4-manifold, show that the field ε[itex]_{ijkl}[/itex]a[itex]^{i}[/itex]b[itex]^{k}[/itex]c[itex]^{l}[/itex] is orthogonal to [itex]\vec{a}[/itex], [itex]\vec{b}[/itex], and [itex]\vec{c}[/itex].

2. Relevant equations

3. The attempt at a solution

I know I have to show that multiplying the field by each individual vector field equals 0, but I don't know how to go about doing this.

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# Show that this field is orthogonal to each vector field.

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