Note that B - A is just equal to B + (-A). A. Since the 2 vectors are in two opposite directions, we write: 4 u + (-6 u) = - 2 u. B. This one is quite tricky. Since I am not that expert in using the tip-to-tail method, I will use the component method. We first solve the components of the vectors: B: (x: 5 m) and (y: 0 m) and for -A: (*note: since we have an opposite direction, the vector will now have an angle of 60° + 180° = 240° and the new direction would be S of W) (x: 7.0cos240°) and (y: 7.0cos240°). Then subtract the components to get the components of the resultant vector: (x: 5m - 7.0cos240° = 8.5 m) and (y: 0 - 7.0sin240° = 6.06 m). Then we now solve the resultant by: R = sqrt ((8.5)^2 + (6.06)^2) = 10.45 m. For the angle, we solve: theta = arctan (6.06m / 8.5m) = 35.44°. So the final answer is: 10.45, 35.44° N of E.
