Question: Prove that every proper affine isometry F(x) = Q x + b of R3, where det Q = +1, is one of the following: (a)

Prove that every proper affine isometry F(x) = Q x + b of R3, where det Q = +1, is one of the following:
(a) A translation x + b,
(b) A rotation centered at some point of R3, or
(c) A screw consisting of a rotation around an axis followed by a translation in the direction of the axis.

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