How to simplify tensor expression with symbolic coeficients?

$Assumptions = {(a | b | c) ∈ Vectors[3], g ∈ Reals}

TensorReduce[g b.a\[Cross]c - g c.b\[Cross]a]

0

$Assumptions=(a|b|c) ∈ Vectors[3] && g ∈ Reals

TensorReduce[g b.a\[Cross]c-g c.b\[Cross]a]
(*0*)

g doesn't have to be Reals. Complexes works too. It just can't be something totally undefined.