When will resultant of the two vectors be at a maximum

when they are in the same direction.

say the first one is 1 in the x direction
the second one is 1 at angle T above x axis
then
x component = 1 + 1 cos T
y component = 1sin T
|V| = sqrt [ (1 + cos T)^2 + sin^2 T ]
sqrt [ 1 + 2 cos T + cos^2 T + sin^2 T ]
=sqrt [ 1 + 2 cos T + 1 ]
biggest when cos T = 1, which is when T = 0
= sqrt 4 = 2