Precalculus, Chapter 6, 6.3, Section 6.3, Problem 38

You need to perform the addition of the vectors u and v,u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u + v = (u_x+v_x)i + (u_y+v_y)j
u + v = (0+3)i + (2+0)j
u + v =3i + 2j
Hence, evaluating the sum of the vectors u and v yields u + v =3i + 2j .
You need to perform the difference of the vectors u and v,u = u_x*i + u_y*j, v = v_x*i + v_y*j , such that:
u - v = (u_x-v_x)i + (u_y-v_y)j
u - v = (0-3)i + (2-0)j
u - v =-3i + 2j
Hence, evaluating the sum of the vectors u and v yields u - v =-3i + 2j.