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For any two vectors ` vec a and vec b` , prove that: `| vec a+ vec b|^2=| vec a|^2+| vec b|^2+2 vec adot vec b`, `| vec a- vec b|^2=| vec a|^2+| vec b|^2-2 vec adot vec b`, `| vec a+ vec b|^2+| vec a- vec b|^2=2(| vec a|^2+| vec b|^2)` and `| vec a+ vec b|^2=| vec a- vec b|^2 iff vec a_|_ vec bdot` Interpret the result geometrically.

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