- #1
bookworm_07
- 4
- 0
Ok I know that isometries preserve distance and in order for a fn to be an isometry || f(u) - f(v) || = || u - v ||
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 don't 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
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 don't 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