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# Parallelogram Law watch

1. Does anyone know how to prove the parallelogram law? i.e.

(x + y)^2 + (x − y)^2 = 2(x)^2 + 2(y)^2

any help would be welcome, thanks
2. (Original post by parks)
Does anyone know how to prove the parallelogram law? i.e.

(x + y)^2 + (x ? y)^2 = 2(x)^2 + 2(y)^2

any help would be welcome, thanks
If you expand the brackets on the LHS the xy terms will cancel and simplify to give the RHS.
3. We were given a hint, use the definition of the Euclidean norm in terms of inner products to prove it. Surely just expanding the other side is too basic to prove it, isnt it? And i forgot the definition of the Euclidean norm in terms of inner products

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