# Verifying equality $(\vec a \times \vec b)^2 = \left| \vec a \times \vec b \right| ^2$

I'm trying to verify the equality $$(\vec a \times \vec b)^2 = \left| \vec a \times \vec b \right| ^2$$ in Mathematica. How can I do it?

• Thank you very much to all of you. – Gennaro Arguzzi Jan 21 '19 at 11:19

Here is another explicit way

veca = {a1, a2, a3};
vecb = {b1, b2, b3};

Cross[veca, vecb].Cross[veca, vecb] - Norm[Cross[veca, vecb]]^2 // Simplify[#, veca~Join~vecb \[Element] Reals] &
0

Try

\$Assumptions = (a | b) \[Element] Vectors[3]
Cross[a, b].Cross[a, b] // TensorExpand
(*-(a.b)^2 + a.a b.b*)