Quickly skimming over this:
We know that w is formed by starting at the origin then moving v, then moving from v and going to w: w = OV + VW
The same logic works for s, we start at the origin and move to v, then we move from v to s: s = OV + VS
Given that |OV| = L1*|VS| where L is some constant it is true that |VS|=L2*|OV| where L2 is some other constant.
Thus: s = OV + VS = OV + L2*OV = (1+L2)*OV
The question states |OV| = Lambda*|VS|, but I think it should have said Lambda*|OV| = |VS|. But I could be wrong.