Ok I know that isometries preserve distance and in order for a fn to be an isometry || f(u) - f(v) || = || u - v ||(adsbygoogle = window.adsbygoogle || []).push({});

and in this question it asks to prove

prove that if an isometry satisfies f(0) = 0 then we have

f(u) x f(v) = +- f(u x v)

and what property of f determines the choice of sign

"x" is the cross product

Now i know that this space must be R^3 because its the cross product

and i know that f(0) = 0 because

|| f(v) - f(u) || = || f(0) - f(0) || = 0

I just dont know how to connect this knowledge to the cross product.

A push in the right direction would be awsome!! I just need a start.

thank you very much

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# Homework Help: Geometry proof

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