
Orthonormal basis
let be a positive oriented orthonormal basis.
Define a new basis
* Show that also is a orthonormal basis.
* determine the coordinates for the vector in the base
and:
i thought this would be the coordinates for the vector u:
=
I need some advice for the first problem on how to show that is an orthonormal basis to.
Thanks!
Edit: dont need help to show that is an orthonormal basis. Figured it out right after i posted :)

your calculations look OK to me, you have a typo u = (1,4,7) not (1,3,7). verifying (f1,f2,f3) is orthogonal is just a matter of computing the 9 inner products, or, you could notice that the change of basis matrix U has the property that U^1 = U^T, and is thus orthogonal, and preseves inner products.

oops missed the typo, guess i need a break :D ... thanks for the help!