hey there.. how am i going to sketch a vector diagram of the given diagram?
is it same like phasor diagram?

btw, what is K? it is the turn winding right?

 

I've never heard the term 'vector diagram' but it sounds to me like phasors, and yes, K would be the turns on the second winding. Often times you set one side of the transformer to one and then solve for K (or a, or whathaveyou). This usually results in a noninteger. From there you can balance the turns ratios to be what you want and integers.