Question: How to do "simple" vector calculation (with example)



I want to calculate the voltage between phase 1 and phase N in an electrical circuit:


The vectorial formula is:

`#mover(mi("U"),mo("→"))`[L1-N]-`#mover(mi("ΔU",mathcolor = "blue"),mo("→",mathcolor = "blue"))`[L1]+`#mover(mi("ΔU",mathcolor = "#339966"),mo("→",mathcolor = "#339966"))`[N] = `#mover(mi("U",mathcolor = "red"),mo("→",mathcolor = "red"))`[L1-N]


Voltage drops are calculated with the current multiplied with the resistance: ΔU = I*Z[L]




-`#mover(mi("I",mathcolor = "blue"),mo("→",mathcolor = "blue"))`[L1]*`#mover(mi("Z",mathcolor = "#ff99cc"),mo("→",mathcolor = "#ff99cc"))`[L]+`#mover(mi("I",mathcolor = "#339966"),mo("→",mathcolor = "#339966"))`[N]*`#mover(mi("Z",mathcolor = "#ff99cc"),mo("→",mathcolor = "#ff99cc"))`[L]+`#mover(mi("U"),mo("→"))`[L1-N] = `#mover(mi("U",mathcolor = "red"),mo("→",mathcolor = "red"))`[L1-N]NULL

This is a real example with realistic values and angles. Note that i have two different vectors with the same index.

This is on purpose and the vector is different. This is because the first vector is before the resistance in the wire and

the one i want to find, is after the resistance in the wire (the red one).:







The negative angles is because i am using my reference which is in 0°. And are the vector to the right of my reference is the angle negative, and is it on the left of my reference is the angle negative. I dont want to explain the vectorial diagram, because i think it will do more confusion than explaining.





My question is, if the formula above is possible to solve in maple?



The result is calculated on my CAS-calulator:


"(U[L1-N])=226 V∠-0.7°"``


The example in Maple:



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