vector + vector?

Well if i and j are unit vectors in x and y directions

U= a i + b j
and
V = c i + d j
then
W = U + V = (a+c) i + (b+d) j
magnitude |W| = sqrt [ (a+c)^ 2 + (b+d)^2 ]
tangent of angle with x axis = (b+d)/(a+c)