7
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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?

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

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

0

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$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.

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