Physics

The resultant of two vectors depends on how aligned they are. When vectors point the same direction ($0°$), they reinforce fully and the resultant is largest; as the angle between them increases, they cancel each other out more, shrinking the resultant. At $180°$ they point opposite ways and cancel as much as possible. The key insight is that the resultant traces a smooth curve from maximum to minimum, following the geometry of vector addition rather than simple arithmetic.

The resultant of two vectors depends on how aligned they are. When vectors point the same direction ($0°$), they reinforce fully and the resultant is largest; as the angle between them increases, they cancel each other out more, shrinking the resultant. At $180°$ they point opposite ways and cancel as much as possible. The key insight is that the resultant traces a smooth curve from maximum to minimum, following the geometry of vector addition rather than simple arithmetic.