Statement :- If a and b be two vectors of equal length, then vector a+b will bisect the angle between a and b.
Proof :
Here OBCA is a parallelogram. Consider triangle OAC and OBC, they both are congruent to each other (OA=OB, because vector a and b are of equal length ; AC=BC ; OC is common between them). So, angle AOC = angle BOC. Therefore we can conclude that OC bisects angle AOB. Hence Proved.
Since ||u|| = 2*||v|| and vector w bisects the angle between u & v. So, w must be u+2v. Therefore $\alpha$=2.