1. The problem statement, all variables and given/known data Ok guys, I'm studying Physics and I started, of course, by learning about vectors. So I have this problem: There are two vectors: A (its length is 3 m) and B (its length is 4 m). I have not other informations about them. I want to know how I can dispose them to get a vector S (which is A + B) such as: a) its length is 7 m. b) its length is 1 m. c) its length is 5 m. Now, I know that the points a and b are obvious but I want a rigorous solution which is valid for point c and for every other length of the vector S. 2. Relevant equations Note: From now on when I write a I mean the length of the vector A. When I write b I mean the length of the vector B. Let's call o the agle between them. Maybe this equation will be useful. cos(o) = (A . B) / (a b) 3. The attempt at a solution I tried but I cannot evaluate the scalar product A . B because it is equals to (a b cos(o)). And if I replace it in the equation I have: cos(o) = (a b cos(o)) / (a b) = cos(o) I need your help.