Question

Given vector A with magnitude 2N and vector B magnitude 4N, what are the minimum and maximum magnitudes of A+B?​

Answer 1

-- If A and B are pointing in exactly opposite directions, then their sum A+B is the minimum possible value.  A+B = 2 N in the same direction as B.

-- If A and B are pointing in exactly the same direction, then their sum A+B is the maximum possible value.  A+B = 6 N in that same direction.