Question

Should a quantity having magnitude and direction be necessarily a vector ?

Answer 1

No because electric current have both magnitude and direction but it is not a vector quantity because the formula of e.c. is V/R and voltage and resistance are scalar quantities.and two scalar quantities can never give a vector quantity .and it follows simple algebra rules.

Answer 2

It is a universal law in physics. If any quantity has direction and magnitude then it ought to be a vector quantity. It is not necessary that a quantity having both direction and magnitude is a vector. If it has both but does not follow vector addition then it is not vector.
Example: electric current has both magnitude and direction.