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
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.
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!