The Law of Cosines is essential for solving vector sums, particularly when determining the resultant of two forces. In the discussion, the forces are represented as 3p and 2p, with the resultant R. When the first force is doubled, the resultant also doubles, indicating a direct relationship between force magnitude and resultant vector. The angle between the two forces can be derived using the formula R² = |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.
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