Faraday tensor

[Genady]

This exercise is from Gravitation by Misner, Thorne, Wheeler. I am concerned here with the second part of it, marked with green:

My answer for the electric field is (e_j, u). For the magnetic field, (e_k, e_i), where i-j-k are in the cyclical order of 1-2-3. Is it correct?

For the reference, here is a components representation of the Faraday tensor in a Lorentz frame:

 

Edited September 6, 2023 by Genady

[Markus Hanke]

I would have answered the same.

Does anyone see a reason why this would be incorrect?

[Genady]

3 hours ago, Markus Hanke said:

I would have answered the same.

Thanks.