Question

what is a quantity with direction and magnitude but is not a vector,just like theta(angle) and why?

Answer 1

We have many quantities which have magnitude and direction but aren’t vectors. Such like electric current, pressure and so on. Though these quantities have both magnitude and direction their directions are not necessary when we define them and that’s why they aren’t vectors (vector requires direction to be defined – always! – and it also has a magnitude.)
Answer: electric current, pressure, etc.