I have been given this question to complete but I have never studied Phasor Diagrams or Load balancing so I am completely stumped by this.

Any advice would be greatly appreciated.

Thank you.

 

learn basic trigonometry

 

This is a situation calling for vector arithmetic. The solution is straightforward but quite tedious.
It looks like part of an electrician licensing examination.

 

Is this your homework or just your personal practice?

 

Ypo cam also do it by super-position. The neutral current will be the vector sum of the contributions by each leg current. At least I think I recall something like that. It was in an AC circuits class back in 1968.

 

The terms Phasor Diagrams and Load Balancing relate to 3 Phase power systems.
I suggest you have a look here for a start. https://en.wikipedia.org/wiki/Three-phase_electric_power

 

It was clear in post #1 that the question was about 3-phase power. And while a knowledge of trig is required it is not sufficient to provide the answers to the question.
The benefits of load balancing are: First, it reduces neutral line current, and second, that it tends to increase system efficiency in several different ways, including more efficient transformer operation (less winding heating) and second, lower conductor losses

 

This is a Homework Question !