The Law of Cosines is used to calculate the magnitude of the resultant vector when adding two vectors, represented as |R| = √(|A|² + |B|² + 2|A||B|cos(θ)), where |A| and |B| are the magnitudes of the vectors and θ is the angle between them. In the case of two forces, if one force is doubled, the resultant vector also doubles, indicating a direct relationship between the magnitudes and the angle. The angle between the two forces can be derived from the equation by rearranging it to isolate cos(θ). Understanding this relationship is crucial for solving vector sum problems effectively. The Law of Cosines provides a systematic approach to determine the resultant vector's magnitude based on the vectors' magnitudes and the angle between them.
