How do you prove that [a+b b+c c+a] = 2 [a b c]?
a, b, c are vectors.

Hiii
You can assume a , b , c to be any vectors in 3D space . And after wards apply the dot and cross product wherever required. It will lead you to the RHS .

But if you want to prove it then assume the 3 vectors to be 3 axis of coordinate and analyse the meaning by mentally drawing images of the processes.

best of Luck