Vectors have a direction too apart from the magnitude.
We have to take care wether the vectors being added are in the sane direction or not before being added.
Eg. in cartitian coordinates, two vectors can be written as:
A = 2i + 3j
B = 5i - 2j
Thus in this notation A and B vectors basically has two components each in i and j direction and those components can be added like normal numbers:
A+B = (2+5)i + (3-2)j = 7i + j