...
The first loop consists of A-C-D-A and the second loop is B-E-C-A-B. Creating vector loops helped to break down the analysis into small chunks that were easier to solve. If we take the first loop as example, the first thing I did was write the vector summation equation, as shown below:
Va + Vb - Vc = 0
where Va is BLUE, Vb is GREEN and Vc is the vector from A to B.
...
After using Euler's equation and splitting the equation into real and imaginary components, we get the following result:
Real: -acos(θA) + bcos(θB) - ccos(θC) = 0
Img: -asin(θA) + bsin(θB) - csin(θC) = 0
Since θC = 0, that simplifies two terms in both real and imaginary equations. Finally, we can solve both of the equations and we get:
