Question

suppose A=3i-2j and B=-j-aj ,what is the value of a such that A+B=2i

Answer 1

Add each component of the vectors respectively:

$$A+B=2i,\\\space\\ (3i-2j)+(-i-aj)=2i,\\ i-j(2+a)=2i.$$

The last is only possible when

$$2+a=0, \\ a=-2.$$