Resultant amplitude of 6 phasors

[OnlinePhysicsTutor]

Homework Statement

This is a problem from one of my students, he is taking an undergrad module in optics. Most of the question is fine but I cannot see a neat solution to part ii

Homework Equations

These are the equations for the topic, but I am not sure if we are missing the relevant equation for part ii

The Attempt at a Solution

The only way I can see is to do it geometrically by calculating components for each of the phasors and find the resultant. But this seem to be far more work than the rest of the questions, so I think I am missing something.

 

[vela]

You can add the phasors in pairs to reduce the problem to a three-phasor problem. Adding three phasors is straightforward.

Edit: Since it's a numerical problem, it's really not very much work to get the answer through the brute-force method you considered.

 

[ehild]

Question i is very easy. Question iii can be answered using symmetry. Draw the phasors in a circle of radius E₀ like in the figure, so as their sum is zero.