4. [10 points] (a) Prove that if f: R³ R³ is an isometry such that f(0,0,0) = (0,0,0), then f preserves dot products, th

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4 10 Points A Prove That If F R R Is An Isometry Such That F 0 0 0 0 0 0 Then F Preserves Dot Products Th 1 (16.52 KiB) Viewed 41 times

4. [10 points] (a) Prove that if f: R³ R³ is an isometry such that f(0,0,0) = (0,0,0), then f preserves dot products, that is f(v). f(w) = v. w for all v,w R³. =V (b) Now prove the converse, namely, that if f: R³ R³ preserves dot products, then it is an isometry fixing the origin.