# How to simplify tensor expression with symbolic coeficients?

I can use Vectors to simplify the following expression:

$Assumptions = (a | b | c) ∈ Vectors[3]; TensorReduce[3 b.a\[Cross]c - 3 c.b\[Cross]a]  which gives me 0, and correct. However, if I change the value "3" into a symbol "g", it fails: $Assumptions = (a | b | c) ∈ Vectors[3];
TensorReduce[g b.a\[Cross]c - g c.b\[Cross]a]


Or

$Assumptions = (a | b | c) ∈ Vectors[3];$Assumptions = g ∈ Reals;
TensorReduce[g b.a\[Cross]c - g c.b\[Cross]a]


Mathematica gives me $g b.a\times c-g c.b\times a$, which should be 0 as well.

How can I do this simplification in Mathematica?

$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

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