If vectorA + vectorB= vectorA=vectorB then find angle between vector a and vector b

The angle between A and B is not defined.

Let vector A = a ; vector B = b.

a+b = a-b, 2b = 0(null vector).

Hence b is a null vector and a is any possible vector.

The catch is that the null vector doesn't have a well defined direction, and hence you cannot find the angle between a and b.