Prove Lorentz Transformations: |E|>|cB| & Angle b/t E & B

[LocationX]

I need to show that:
1. if E is $\perp$ to B in one Lorentz frame, it is $\perp$ in all Lorentz frames
2. $|E|>|cB|$ in L. frame, $|E|>|cB|$ in all L. frame
3. Angle b/t E and B is acute/obtuse in L. frame, it is acute/obtuse in all L. frame
4. E is $\perp$ to B but $|E|\neq|cB|$, then there is a frame which the field is purely electric or magnetic

Attempt:
1. I believe I just show that $\bar{E} \cdot \bar{B} =E \cdot B$
2. I believe I just show $\bar{E}^2-c^2 \bar{B}^2 =E^2-B^2c^2$ so that if $|E|>|cB|$, then $\bar{E}^2-c^2 \bar{B}^2$ is positive and thus $E^2-B^2c^2$ has to be positive, thus, $|E|>|cB|$ in all frames.

Not too sure where to start for 3 and 4. Open to suggestions, also it would be great if someone could check my approach for 1 and 2. thanks.

 

[tiny-tim]

3. Angle b/t E and B is acute/obtuse in L. frame, it is acute/obtuse in all L. frame
4. E is $\perp$ to B but $|E|\neq|cB|$, then there is a frame which the field is purely electric or magnetic

Hi LocationX!

Your answers to 1 and 2 seem fine.

3 should be similar to 1 … what is the sign of E.B if the angle between is acute?

4: I suggest you start with the simple case of |E| > c|B|, and B and E along the x-direction and y-direction respectively, and see what happens when you transform parallel to the x-direction.