(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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Show that this field is orthogonal to each vector field.

**Physics Forums | Science Articles, Homework Help, Discussion**