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Let $a,b,c$ be three different points in a vector space $E$ over the real numbers, and with an inner product. Let $d$ be the metric defined by the inner product. Prove that if: $ d(a,c) = d(a,b)+d(b,c) $ then $ c= tb + (1-t)a $ for some $ t > 1 $.

The only thing I could do , is write the equality in terms of the dot product, but I don“t know how to use the new equality :/

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