Let u,v and w be fixed, but unknown vectors in RnRn. (The solution is the same whether n=2,3n=2,3 or n≥4n≥4.) Prove that if those vectors are all orthogonal to each other, then ∥u+v+w∥^2=∥u∥^2+∥v∥^2+∥w∥^2

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